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Номер 534, страница 155 - гдз по алгебре 9 класс учебник Солтан, Солтан
Авторы: Солтан Г. Н., Солтан А. Е., Жумадилова А. Ж.
Тип: Учебник
Издательство: Кокшетау
Год издания: 2019 - 2026
ISBN: 978-601-317-424-2
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 9 классе
IV. Тригонометрия. 21. Градусная и радианная меры углов и дуг - номер 534, страница 155.
App\Models\Task {#1024 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108264 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "155" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-534" "field_display_title" => "534" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "IV. Тригонометрия" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "147" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1033 #items: array:1 [ 0 => App\Models\Book {#1030 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1032 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1032} "field_class" => Illuminate\Database\Eloquent\Collection {#1035} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037} "field_author" => Illuminate\Database\Eloquent\Collection {#1039} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044} "field_country" => Illuminate\Database\Eloquent\Collection {#1046} "field_city" => Illuminate\Database\Eloquent\Collection {#1048} "field_series" => Illuminate\Database\Eloquent\Collection {#1050} "field_umk" => Illuminate\Database\Eloquent\Collection {#1051} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "IV. Тригонометрия" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "147" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1033} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1060} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:2 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1062 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107663 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "21. Градусная и радианная меры углов и дуг" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "148" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Book {#1065 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1066} "field_class" => Illuminate\Database\Eloquent\Collection {#1068} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1070} "field_author" => Illuminate\Database\Eloquent\Collection {#1072} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_country" => Illuminate\Database\Eloquent\Collection {#1079} "field_city" => Illuminate\Database\Eloquent\Collection {#1081} "field_series" => Illuminate\Database\Eloquent\Collection {#1083} "field_umk" => Illuminate\Database\Eloquent\Collection {#1084} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1086} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1093 #items: array:1 [ 0 => App\Models\Branch {#1094 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "IV. Тригонометрия" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_page_start" => "147" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1096 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1097 …2} ] #original: array:24 [ "id" => 1107662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "IV. Тригонометрия" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_page_start" => "147" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1096 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1097 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107663 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "21. Градусная и радианная меры углов и дуг" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_page_start" => "148" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1064} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1093} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:3 [ 0 => App\Models\Element {#1099 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1276889 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Edition {#1101 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108264" "type" => "task" ] "text" => "<p><strong>534.</strong> Укажите в радианах все углы, соответствующие точкам координатной окружности, изображенным на рисунке 54.</p><p><strong>а)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point B (60 degrees) --><circle cx="70.00" cy="15.36" r="1.5" fill="black"/><text x="72" y="15" font-size="10">B</text><line x1="50" y1="50" x2="70.00" y2="15.36" stroke="black" stroke-width="1"/><!-- Point C (120 degrees) --><circle cx="30.00" cy="15.36" r="1.5" fill="black"/><text x="25" y="15" font-size="10">C</text><line x1="50" y1="50" x2="30.00" y2="15.36" stroke="black" stroke-width="1"/><!-- Angle labels and markers --><text x="60" y="38" font-size="9">60°</text><text x="40" y="38" font-size="9">60°</text><line x1="50" y1="50" x2="50.00" y2="43.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="46.06" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="50.00" y2="43.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="46.50" y2="46.06" stroke="black" stroke-width="1"/></svg><p><strong>б)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point D (30 degrees) --><circle cx="84.64" cy="30.00" r="1.5" fill="black"/><text x="86" y="29" font-size="10">D</text><line x1="50" y1="50" x2="84.64" y2="30.00" stroke="black" stroke-width="1"/><!-- Point K (-30 degrees or 330 degrees) --><circle cx="84.64" cy="70.00" r="1.5" fill="black"/><text x="86" y="70" font-size="10">K</text><line x1="50" y1="50" x2="84.64" y2="70.00" stroke="black" stroke-width="1"/><!-- Angle labels and markers --><text x="65" y="38" font-size="9">30°</text><text x="65" y="62" font-size="9">30°</text><line x1="50" y1="50" x2="50.00" y2="43.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="46.06" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="50.00" y2="57.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="53.94" stroke="black" stroke-width="1"/></svg><p><strong>в)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point M (135 degrees) --><circle cx="21.72" cy="21.72" r="1.5" fill="black"/><text x="18" y="18" font-size="10">M</text><line x1="50" y1="50" x2="21.72" y2="21.72" stroke="black" stroke-width="1"/><!-- Point N (-45 degrees or 315 degrees) --><circle cx="78.28" cy="78.28" r="1.5" fill="black"/><text x="80" y="80" font-size="10">N</text><line x1="50" y1="50" x2="78.28" y2="78.28" stroke="black" stroke-width="1"/><!-- Angle label and markers --><text x="65" y="65" font-size="9">45°</text><line x1="50" y1="50" x2="50.00" y2="57.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="53.94" stroke="black" stroke-width="1"/></svg><p><strong>г)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point E (90 degrees) --><circle cx="50.00" cy="10.00" r="1.5" fill="black"/><text x="52" y="10" font-size="10">E</text><!-- Point F (270 degrees) --><circle cx="50.00" cy="90.00" r="1.5" fill="black"/><text x="52" y="90" font-size="10">F</text></svg><p>Рисунок 54</p>" "img" => array:1 [ 0 => array:5 [ "name" => "534-1.jpg" "alt" => null "width" => "1559" "height" => 648 "path" => "/media/algebra_09/soltan-u19/0-1/534-1.webp?ts=1752834553" ] ] ] #original: array:7 [ "id" => 1276889 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100} "task" => array:2 [ "refs" => "1108264" "type" => "task" ] "text" => "<p><strong>534.</strong> Укажите в радианах все углы, соответствующие точкам координатной окружности, изображенным на рисунке 54.</p><p><strong>а)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point B (60 degrees) --><circle cx="70.00" cy="15.36" r="1.5" fill="black"/><text x="72" y="15" font-size="10">B</text><line x1="50" y1="50" x2="70.00" y2="15.36" stroke="black" stroke-width="1"/><!-- Point C (120 degrees) --><circle cx="30.00" cy="15.36" r="1.5" fill="black"/><text x="25" y="15" font-size="10">C</text><line x1="50" y1="50" x2="30.00" y2="15.36" stroke="black" stroke-width="1"/><!-- Angle labels and markers --><text x="60" y="38" font-size="9">60°</text><text x="40" y="38" font-size="9">60°</text><line x1="50" y1="50" x2="50.00" y2="43.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="46.06" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="50.00" y2="43.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="46.50" y2="46.06" stroke="black" stroke-width="1"/></svg><p><strong>б)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point D (30 degrees) --><circle cx="84.64" cy="30.00" r="1.5" fill="black"/><text x="86" y="29" font-size="10">D</text><line x1="50" y1="50" x2="84.64" y2="30.00" stroke="black" stroke-width="1"/><!-- Point K (-30 degrees or 330 degrees) --><circle cx="84.64" cy="70.00" r="1.5" fill="black"/><text x="86" y="70" font-size="10">K</text><line x1="50" y1="50" x2="84.64" y2="70.00" stroke="black" stroke-width="1"/><!-- Angle labels and markers --><text x="65" y="38" font-size="9">30°</text><text x="65" y="62" font-size="9">30°</text><line x1="50" y1="50" x2="50.00" y2="43.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="46.06" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="50.00" y2="57.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="53.94" stroke="black" stroke-width="1"/></svg><p><strong>в)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point M (135 degrees) --><circle cx="21.72" cy="21.72" r="1.5" fill="black"/><text x="18" y="18" font-size="10">M</text><line x1="50" y1="50" x2="21.72" y2="21.72" stroke="black" stroke-width="1"/><!-- Point N (-45 degrees or 315 degrees) --><circle cx="78.28" cy="78.28" r="1.5" fill="black"/><text x="80" y="80" font-size="10">N</text><line x1="50" y1="50" x2="78.28" y2="78.28" stroke="black" stroke-width="1"/><!-- Angle label and markers --><text x="65" y="65" font-size="9">45°</text><line x1="50" y1="50" x2="50.00" y2="57.00" stroke="black" stroke-width="1"/><line x1="50" y1="50" x2="53.50" y2="53.94" stroke="black" stroke-width="1"/></svg><p><strong>г)</strong></p><svg xmlns="http://www.w3.org/2000/svg" width="150" height="150" viewBox="0 0 100 100"><!-- Common elements: Axes and Origin --><line x1="10" y1="50" x2="90" y2="50" stroke="black" stroke-width="1"/><polyline points="87,47 90,50 87,53" stroke="black" fill="none" stroke-width="1"/><line x1="50" y1="10" x2="50" y2="90" stroke="black" stroke-width="1"/><polyline points="47,13 50,10 53,13" stroke="black" fill="none" stroke-width="1"/><text x="52" y="58" font-size="10">O</text><text x="92" y="58" font-size="10">x</text><text x="52" y="18" font-size="10">y</text><!-- Circle --><circle cx="50" cy="50" r="40" fill="none" stroke="black" stroke-width="1"/><!-- Point E (90 degrees) --><circle cx="50.00" cy="10.00" r="1.5" fill="black"/><text x="52" y="10" font-size="10">E</text><!-- Point F (270 degrees) --><circle cx="50.00" cy="90.00" r="1.5" fill="black"/><text x="52" y="90" font-size="10">F</text></svg><p>Рисунок 54</p>" "img" => array:1 [ 0 => array:5 [ "name" => "534-1.jpg" "alt" => null "width" => "1559" "height" => 648 "path" => "/media/algebra_09/soltan-u19/0-1/534-1.webp?ts=1752834553" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1107 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1278180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Edition {#1109 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108264" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "534-1.jpg" "alt" => null "width" => "831" "height" => 895 "path" => "/media/algebra_09/soltan-u19/1-1/534-1.webp?ts=1752831313" ] ] ] #original: array:6 [ "id" => 1278180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108} "task" => array:2 [ "refs" => "1108264" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "534-1.jpg" "alt" => null "width" => "831" "height" => 895 "path" => "/media/algebra_09/soltan-u19/1-1/534-1.webp?ts=1752831313" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1115 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1554135 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Edition {#1117 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108264" "type" => "task" ] "text" => "<p><strong>а)</strong> Для нахождения углов, соответствующих точкам B и C, проанализируем рисунок. Углы по $60^\circ$ отложены от положительного направления оси Oy. Угол, соответствующий положительному направлению оси Oy, равен $90^\circ$ или $\frac{\pi}{2}$ радиан.<br>Точка B находится в первой четверти. Угол для точки B меньше $90^\circ$ на $60^\circ$, то есть: $\alpha_B = 90^\circ - 60^\circ = 30^\circ$.<br>Переведем в радианы: $30^\circ = 30 \cdot \frac{\pi}{180} = \frac{\pi}{6}$ радиан.<br>Точка C находится во второй четверти. Угол для точки C больше $90^\circ$ на $60^\circ$, то есть: $\alpha_C = 90^\circ + 60^\circ = 150^\circ$.<br>Переведем в радианы: $150^\circ = 150 \cdot \frac{\pi}{180} = \frac{5\pi}{6}$ радиан.<br>Так как полный оборот по окружности составляет $2\pi$ радиан, то для нахождения всех углов необходимо к найденным значениям прибавить $2\pi k$, где $k$ — любое целое число ($k \in \mathbb{Z}$).<br>Ответ: Для точки B: $\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$. Для точки C: $\frac{5\pi}{6} + 2\pi k, k \in \mathbb{Z}$.</p><p><strong>б)</strong> Углы для точек D и K отложены от положительного направления оси Ox.<br>Точка D находится в первой четверти. Угол отложен против часовой стрелки, поэтому он положительный: $\alpha_D = 30^\circ$.<br>Переведем в радианы: $30^\circ = 30 \cdot \frac{\pi}{180} = \frac{\pi}{6}$ радиан.<br>Точка K находится в четвертой четверти. Угол отложен по часовой стрелке, поэтому он отрицательный: $\alpha_K = -30^\circ$.<br>Переведем в радианы: $-30^\circ = -30 \cdot \frac{\pi}{180} = -\frac{\pi}{6}$ радиан.<br>Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.<br>Ответ: Для точки D: $\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$. Для точки K: $-\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$.</p><p><strong>в)</strong> Точка N находится в четвертой четверти. Угол для нее отложен от положительного направления оси Ox по часовой стрелке и равен $45^\circ$, значит, его значение $\alpha_N = -45^\circ$.<br>Переведем в радианы: $-45^\circ = -45 \cdot \frac{\pi}{180} = -\frac{\pi}{4}$ радиан.<br>Точка M диаметрально противоположна точке N, так как отрезок MN проходит через центр окружности. Это значит, что их углы отличаются на $180^\circ$ (или $\pi$ радиан).<br>Угол для точки M: $\alpha_M = -45^\circ + 180^\circ = 135^\circ$.<br>Переведем в радианы: $135^\circ = 135 \cdot \frac{\pi}{180} = \frac{3\pi}{4}$ радиан.<br>Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.<br>Ответ: Для точки M: $\frac{3\pi}{4} + 2\pi k, k \in \mathbb{Z}$. Для точки N: $-\frac{\pi}{4} + 2\pi k, k \in \mathbb{Z}$.</p><p><strong>г)</strong> Точки E и F лежат на оси Oy.<br>Точка E находится на положительной части оси Oy. Этому положению соответствует угол $90^\circ$.<br>В радианах: $90^\circ = \frac{\pi}{2}$ радиан.<br>Точка F находится на отрицательной части оси Oy. Этому положению соответствует угол $270^\circ$ или, что то же самое при движении по часовой стрелке, $-90^\circ$.<br>В радианах: $270^\circ = \frac{3\pi}{2}$ радиан, или $-90^\circ = -\frac{\pi}{2}$ радиан.<br>Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.<br>Ответ: Для точки E: $\frac{\pi}{2} + 2\pi k, k \in \mathbb{Z}$. Для точки F: $\frac{3\pi}{2} + 2\pi k$ (или $-\frac{\pi}{2} + 2\pi k$), $k \in \mathbb{Z}$.</p>" ] #original: array:6 [ "id" => 1554135 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116} "task" => array:2 [ "refs" => "1108264" "type" => "task" ] "text" => "<p><strong>а)</strong> Для нахождения углов, соответствующих точкам B и C, проанализируем рисунок. Углы по $60^\circ$ отложены от положительного направления оси Oy. Угол, соответствующий положительному направлению оси Oy, равен $90^\circ$ или $\frac{\pi}{2}$ радиан.<br>Точка B находится в первой четверти. Угол для точки B меньше $90^\circ$ на $60^\circ$, то есть: $\alpha_B = 90^\circ - 60^\circ = 30^\circ$.<br>Переведем в радианы: $30^\circ = 30 \cdot \frac{\pi}{180} = \frac{\pi}{6}$ радиан.<br>Точка C находится во второй четверти. Угол для точки C больше $90^\circ$ на $60^\circ$, то есть: $\alpha_C = 90^\circ + 60^\circ = 150^\circ$.<br>Переведем в радианы: $150^\circ = 150 \cdot \frac{\pi}{180} = \frac{5\pi}{6}$ радиан.<br>Так как полный оборот по окружности составляет $2\pi$ радиан, то для нахождения всех углов необходимо к найденным значениям прибавить $2\pi k$, где $k$ — любое целое число ($k \in \mathbb{Z}$).<br>Ответ: Для точки B: $\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$. Для точки C: $\frac{5\pi}{6} + 2\pi k, k \in \mathbb{Z}$.</p><p><strong>б)</strong> Углы для точек D и K отложены от положительного направления оси Ox.<br>Точка D находится в первой четверти. Угол отложен против часовой стрелки, поэтому он положительный: $\alpha_D = 30^\circ$.<br>Переведем в радианы: $30^\circ = 30 \cdot \frac{\pi}{180} = \frac{\pi}{6}$ радиан.<br>Точка K находится в четвертой четверти. Угол отложен по часовой стрелке, поэтому он отрицательный: $\alpha_K = -30^\circ$.<br>Переведем в радианы: $-30^\circ = -30 \cdot \frac{\pi}{180} = -\frac{\pi}{6}$ радиан.<br>Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.<br>Ответ: Для точки D: $\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$. Для точки K: $-\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$.</p><p><strong>в)</strong> Точка N находится в четвертой четверти. Угол для нее отложен от положительного направления оси Ox по часовой стрелке и равен $45^\circ$, значит, его значение $\alpha_N = -45^\circ$.<br>Переведем в радианы: $-45^\circ = -45 \cdot \frac{\pi}{180} = -\frac{\pi}{4}$ радиан.<br>Точка M диаметрально противоположна точке N, так как отрезок MN проходит через центр окружности. Это значит, что их углы отличаются на $180^\circ$ (или $\pi$ радиан).<br>Угол для точки M: $\alpha_M = -45^\circ + 180^\circ = 135^\circ$.<br>Переведем в радианы: $135^\circ = 135 \cdot \frac{\pi}{180} = \frac{3\pi}{4}$ радиан.<br>Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.<br>Ответ: Для точки M: $\frac{3\pi}{4} + 2\pi k, k \in \mathbb{Z}$. Для точки N: $-\frac{\pi}{4} + 2\pi k, k \in \mathbb{Z}$.</p><p><strong>г)</strong> Точки E и F лежат на оси Oy.<br>Точка E находится на положительной части оси Oy. Этому положению соответствует угол $90^\circ$.<br>В радианах: $90^\circ = \frac{\pi}{2}$ радиан.<br>Точка F находится на отрицательной части оси Oy. Этому положению соответствует угол $270^\circ$ или, что то же самое при движении по часовой стрелке, $-90^\circ$.<br>В радианах: $270^\circ = \frac{3\pi}{2}$ радиан, или $-90^\circ = -\frac{\pi}{2}$ радиан.<br>Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.<br>Ответ: Для точки E: $\frac{\pi}{2} + 2\pi k, k \in \mathbb{Z}$. Для точки F: $\frac{3\pi}{2} + 2\pi k$ (или $-\frac{\pi}{2} + 2\pi k$), $k \in \mathbb{Z}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108265" "type" => "task" ] "previous" => array:2 [ "refs" => "1108263" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1124 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Term {#1128 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1129 #items: array:1 [ 0 => App\Models\Term {#1130 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ …6] "field_translit" => "Kokshetau" ] #original: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ …6] "field_translit" => "Kokshetau" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:3 [ 0 => App\Models\Term {#1132 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1133 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1134 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1125} "field_class" => Illuminate\Database\Eloquent\Collection {#1127} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1129} "field_author" => Illuminate\Database\Eloquent\Collection {#1131} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1135} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1136} "field_country" => Illuminate\Database\Eloquent\Collection {#1138} "field_city" => Illuminate\Database\Eloquent\Collection {#1140} "field_series" => Illuminate\Database\Eloquent\Collection {#1142} "field_umk" => Illuminate\Database\Eloquent\Collection {#1143} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1144} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1148} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1149} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1150} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1151} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1456 #items: array:1 [ 0 => App\Models\BookPage {#1155 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1097897 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "155" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-155" "field_display_title" => "155" "field_folder" => "folder1" "field_image_name" => "155" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1159 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1158 #items: array:1 [ 0 => App\Models\Book {#1160 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1188 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1189 #items: array:1 [ 0 => App\Models\Element {#1190 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1261048 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1261048 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1097898" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097896" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1198 #items: array:6 [ 0 => App\Models\Task {#1199 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108259 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "155" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-529" "field_display_title" => "529" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1202 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1203 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1236 …2} "content" => Illuminate\Database\Eloquent\Collection {#1273 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1298 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108259 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "155" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-529" "field_display_title" => "529" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1202 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1203 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1236 …2} "content" => Illuminate\Database\Eloquent\Collection {#1273 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1298 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1299 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108260 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "155" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-530" "field_display_title" => "530" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1300 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1301 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1302 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1303 …2} "content" => Illuminate\Database\Eloquent\Collection {#1304 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1329 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108260 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "155" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-530" "field_display_title" => "530" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1300 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1301 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1302 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1303 …2} "content" => Illuminate\Database\Eloquent\Collection {#1304 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => 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№534 (с. 155)
Условие. №534 (с. 155)
скриншот условия
534. Укажите в радианах все углы, соответствующие точкам координатной окружности, изображенным на рисунке 54.
а)
б)
в)
г)
Рисунок 54
Решение. №534 (с. 155)
Решение 2 (rus). №534 (с. 155)
а) Для нахождения углов, соответствующих точкам B и C, проанализируем рисунок. Углы по $60^\circ$ отложены от положительного направления оси Oy. Угол, соответствующий положительному направлению оси Oy, равен $90^\circ$ или $\frac{\pi}{2}$ радиан.
Точка B находится в первой четверти. Угол для точки B меньше $90^\circ$ на $60^\circ$, то есть: $\alpha_B = 90^\circ - 60^\circ = 30^\circ$.
Переведем в радианы: $30^\circ = 30 \cdot \frac{\pi}{180} = \frac{\pi}{6}$ радиан.
Точка C находится во второй четверти. Угол для точки C больше $90^\circ$ на $60^\circ$, то есть: $\alpha_C = 90^\circ + 60^\circ = 150^\circ$.
Переведем в радианы: $150^\circ = 150 \cdot \frac{\pi}{180} = \frac{5\pi}{6}$ радиан.
Так как полный оборот по окружности составляет $2\pi$ радиан, то для нахождения всех углов необходимо к найденным значениям прибавить $2\pi k$, где $k$ — любое целое число ($k \in \mathbb{Z}$).
Ответ: Для точки B: $\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$. Для точки C: $\frac{5\pi}{6} + 2\pi k, k \in \mathbb{Z}$.
б) Углы для точек D и K отложены от положительного направления оси Ox.
Точка D находится в первой четверти. Угол отложен против часовой стрелки, поэтому он положительный: $\alpha_D = 30^\circ$.
Переведем в радианы: $30^\circ = 30 \cdot \frac{\pi}{180} = \frac{\pi}{6}$ радиан.
Точка K находится в четвертой четверти. Угол отложен по часовой стрелке, поэтому он отрицательный: $\alpha_K = -30^\circ$.
Переведем в радианы: $-30^\circ = -30 \cdot \frac{\pi}{180} = -\frac{\pi}{6}$ радиан.
Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.
Ответ: Для точки D: $\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$. Для точки K: $-\frac{\pi}{6} + 2\pi k, k \in \mathbb{Z}$.
в) Точка N находится в четвертой четверти. Угол для нее отложен от положительного направления оси Ox по часовой стрелке и равен $45^\circ$, значит, его значение $\alpha_N = -45^\circ$.
Переведем в радианы: $-45^\circ = -45 \cdot \frac{\pi}{180} = -\frac{\pi}{4}$ радиан.
Точка M диаметрально противоположна точке N, так как отрезок MN проходит через центр окружности. Это значит, что их углы отличаются на $180^\circ$ (или $\pi$ радиан).
Угол для точки M: $\alpha_M = -45^\circ + 180^\circ = 135^\circ$.
Переведем в радианы: $135^\circ = 135 \cdot \frac{\pi}{180} = \frac{3\pi}{4}$ радиан.
Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.
Ответ: Для точки M: $\frac{3\pi}{4} + 2\pi k, k \in \mathbb{Z}$. Для точки N: $-\frac{\pi}{4} + 2\pi k, k \in \mathbb{Z}$.
г) Точки E и F лежат на оси Oy.
Точка E находится на положительной части оси Oy. Этому положению соответствует угол $90^\circ$.
В радианах: $90^\circ = \frac{\pi}{2}$ радиан.
Точка F находится на отрицательной части оси Oy. Этому положению соответствует угол $270^\circ$ или, что то же самое при движении по часовой стрелке, $-90^\circ$.
В радианах: $270^\circ = \frac{3\pi}{2}$ радиан, или $-90^\circ = -\frac{\pi}{2}$ радиан.
Общая формула для всех углов, соответствующих этим точкам, получается добавлением $2\pi k, k \in \mathbb{Z}$.
Ответ: Для точки E: $\frac{\pi}{2} + 2\pi k, k \in \mathbb{Z}$. Для точки F: $\frac{3\pi}{2} + 2\pi k$ (или $-\frac{\pi}{2} + 2\pi k$), $k \in \mathbb{Z}$.
Другие задания:
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