gdz.top
Номер 524, страница 154 - 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 524, страница 154.
App\Models\Task {#1030 // 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" => 1108254 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-524" "field_display_title" => "524" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #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 {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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 {#1047 #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 {#1078 #items: array:1 [ 0 => App\Models\Book {#1048 #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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1049 #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 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "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 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1055 #items: array:3 [ 0 => App\Models\Term {#1056 #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 {#1057 #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 {#1058 #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 {#1059 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "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 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1066 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1071 #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 {#1072 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1075 #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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053} "field_author" => Illuminate\Database\Eloquent\Collection {#1055} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060} "field_country" => Illuminate\Database\Eloquent\Collection {#1062} "field_city" => Illuminate\Database\Eloquent\Collection {#1064} "field_series" => Illuminate\Database\Eloquent\Collection {#1066} "field_umk" => Illuminate\Database\Eloquent\Collection {#1067} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1071} "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 {#1072} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1073} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1074} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1075} "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 {#1076 #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 {#1047} "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 {#1078} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1076} ] #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 {#1105 #items: array:2 [ 0 => App\Models\Branch {#1113 #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 {#1114 #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 {#1115 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116 #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 {#1114} "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 {#1115} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116} ] #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\Branch {#1117 #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 {#1118 #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 {#1119 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #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 {#1118} "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 {#1119} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120} ] #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 {#1102 #items: array:3 [ 0 => App\Models\Element {#1095 #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" => 1276879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Edition {#1094 #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 {#1092 #items: array:1 [ …1] #escapeWhenCastingToString: false } "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 {#1090 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "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 {#1092} "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 {#1090} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088} "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" => "1108254" "type" => "task" ] "text" => "<p><strong>524.</strong> Найдите радианную меру угла поворота, заданного в градусах:</p><p><strong>а)</strong> $18^\circ$, $27^\circ$, $30^\circ$, $45^\circ$, $60^\circ$;</p><p><strong>б)</strong> $90^\circ$, $120^\circ$, $135^\circ$, $150^\circ$;</p><p><strong>в)</strong> $210^\circ$, $225^\circ$, $270^\circ$, $300^\circ$;</p><p><strong>г)</strong> $1100^\circ$, $1440^\circ$, $3330^\circ$, $7380^\circ$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "524-1.jpg" "alt" => null "width" => "1527" "height" => 259 "path" => "/media/algebra_09/soltan-u19/0-1/524-1.webp?ts=1752834530" ] ] ] #original: array:7 [ "id" => 1276879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087} "task" => array:2 [ "refs" => "1108254" "type" => "task" ] "text" => "<p><strong>524.</strong> Найдите радианную меру угла поворота, заданного в градусах:</p><p><strong>а)</strong> $18^\circ$, $27^\circ$, $30^\circ$, $45^\circ$, $60^\circ$;</p><p><strong>б)</strong> $90^\circ$, $120^\circ$, $135^\circ$, $150^\circ$;</p><p><strong>в)</strong> $210^\circ$, $225^\circ$, $270^\circ$, $300^\circ$;</p><p><strong>г)</strong> $1100^\circ$, $1440^\circ$, $3330^\circ$, $7380^\circ$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "524-1.jpg" "alt" => null "width" => "1527" "height" => 259 "path" => "/media/algebra_09/soltan-u19/0-1/524-1.webp?ts=1752834530" ] ] ] #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 {#1089 #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" => 1278170 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Edition {#1086 #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 {#1081 #items: array:1 [ …1] #escapeWhenCastingToString: false } "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 {#1084 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "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 {#1081} "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 {#1084} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1083} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1082} "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" => "1108254" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "524-1.jpg" "alt" => null "width" => "1234" "height" => 1385 "path" => "/media/algebra_09/soltan-u19/1-1/524-1.webp?ts=1752831280" ] 1 => array:5 [ "name" => "524-2.jpg" "alt" => null "width" => "1292" "height" => 664 "path" => "/media/algebra_09/soltan-u19/1-1/524-2.webp?ts=1752831280" ] ] ] #original: array:6 [ "id" => 1278170 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1041} "task" => array:2 [ "refs" => "1108254" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "524-1.jpg" "alt" => null "width" => "1234" "height" => 1385 "path" => "/media/algebra_09/soltan-u19/1-1/524-1.webp?ts=1752831280" ] 1 => array:5 [ "name" => "524-2.jpg" "alt" => null "width" => "1292" "height" => 664 "path" => "/media/algebra_09/soltan-u19/1-1/524-2.webp?ts=1752831280" ] ] ] #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 {#1079 #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" => 1554125 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Edition {#1080 #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 {#1040 #items: array:1 [ …1] #escapeWhenCastingToString: false } "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 {#1043 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1034 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "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 {#1040} "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 {#1043} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1034} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1104} "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" => "1108254" "type" => "task" ] "text" => "<p>Для перевода градусной меры угла в радианную используется формула, связывающая градусы и радианы, исходя из того, что $180^{\circ}$ равны $ \pi $ радиан:</p><p>$ \alpha_{рад} = \alpha_{град} \cdot \frac{\pi}{180^{\circ}} $</p><p>Где $ \alpha_{рад} $ — мера угла в радианах, а $ \alpha_{град} $ — мера угла в градусах.</p><p><strong>а)</strong></p><p>$ 18^{\circ} = 18 \cdot \frac{\pi}{180} = \frac{18\pi}{180} = \frac{\pi}{10} $ рад</p><p>$ 27^{\circ} = 27 \cdot \frac{\pi}{180} = \frac{27\pi}{180} = \frac{3\pi}{20} $ рад (сокращаем на 9)</p><p>$ 30^{\circ} = 30 \cdot \frac{\pi}{180} = \frac{30\pi}{180} = \frac{\pi}{6} $ рад</p><p>$ 45^{\circ} = 45 \cdot \frac{\pi}{180} = \frac{45\pi}{180} = \frac{\pi}{4} $ рад</p><p>$ 60^{\circ} = 60 \cdot \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3} $ рад</p><p><strong>Ответ:</strong> $ \frac{\pi}{10} $, $ \frac{3\pi}{20} $, $ \frac{\pi}{6} $, $ \frac{\pi}{4} $, $ \frac{\pi}{3} $.</p><p><strong>б)</strong></p><p>$ 90^{\circ} = 90 \cdot \frac{\pi}{180} = \frac{90\pi}{180} = \frac{\pi}{2} $ рад</p><p>$ 120^{\circ} = 120 \cdot \frac{\pi}{180} = \frac{120\pi}{180} = \frac{2\pi}{3} $ рад (сокращаем на 60)</p><p>$ 135^{\circ} = 135 \cdot \frac{\pi}{180} = \frac{135\pi}{180} = \frac{3\pi}{4} $ рад (сокращаем на 45)</p><p>$ 150^{\circ} = 150 \cdot \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6} $ рад (сокращаем на 30)</p><p><strong>Ответ:</strong> $ \frac{\pi}{2} $, $ \frac{2\pi}{3} $, $ \frac{3\pi}{4} $, $ \frac{5\pi}{6} $.</p><p><strong>в)</strong></p><p>$ 210^{\circ} = 210 \cdot \frac{\pi}{180} = \frac{210\pi}{180} = \frac{7\pi}{6} $ рад (сокращаем на 30)</p><p>$ 225^{\circ} = 225 \cdot \frac{\pi}{180} = \frac{225\pi}{180} = \frac{5\pi}{4} $ рад (сокращаем на 45)</p><p>$ 270^{\circ} = 270 \cdot \frac{\pi}{180} = \frac{270\pi}{180} = \frac{3\pi}{2} $ рад (сокращаем на 90)</p><p>$ 300^{\circ} = 300 \cdot \frac{\pi}{180} = \frac{300\pi}{180} = \frac{5\pi}{3} $ рад (сокращаем на 60)</p><p><strong>Ответ:</strong> $ \frac{7\pi}{6} $, $ \frac{5\pi}{4} $, $ \frac{3\pi}{2} $, $ \frac{5\pi}{3} $.</p><p><strong>г)</strong></p><p>$ 1100^{\circ} = 1100 \cdot \frac{\pi}{180} = \frac{1100\pi}{180} = \frac{110\pi}{18} = \frac{55\pi}{9} $ рад (сокращаем на 20)</p><p>$ 1440^{\circ} = 1440 \cdot \frac{\pi}{180} = \frac{1440\pi}{180} = \frac{144\pi}{18} = 8\pi $ рад (сокращаем на 180)</p><p>$ 3330^{\circ} = 3330 \cdot \frac{\pi}{180} = \frac{3330\pi}{180} = \frac{333\pi}{18} = \frac{37\pi}{2} $ рад (сокращаем на 90)</p><p>$ 7380^{\circ} = 7380 \cdot \frac{\pi}{180} = \frac{7380\pi}{180} = \frac{738\pi}{18} = 41\pi $ рад (сокращаем на 180)</p><p><strong>Ответ:</strong> $ \frac{55\pi}{9} $, $ 8\pi $, $ \frac{37\pi}{2} $, $ 41\pi $.</p>" ] #original: array:6 [ "id" => 1554125 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108} "task" => array:2 [ "refs" => "1108254" "type" => "task" ] "text" => "<p>Для перевода градусной меры угла в радианную используется формула, связывающая градусы и радианы, исходя из того, что $180^{\circ}$ равны $ \pi $ радиан:</p><p>$ \alpha_{рад} = \alpha_{град} \cdot \frac{\pi}{180^{\circ}} $</p><p>Где $ \alpha_{рад} $ — мера угла в радианах, а $ \alpha_{град} $ — мера угла в градусах.</p><p><strong>а)</strong></p><p>$ 18^{\circ} = 18 \cdot \frac{\pi}{180} = \frac{18\pi}{180} = \frac{\pi}{10} $ рад</p><p>$ 27^{\circ} = 27 \cdot \frac{\pi}{180} = \frac{27\pi}{180} = \frac{3\pi}{20} $ рад (сокращаем на 9)</p><p>$ 30^{\circ} = 30 \cdot \frac{\pi}{180} = \frac{30\pi}{180} = \frac{\pi}{6} $ рад</p><p>$ 45^{\circ} = 45 \cdot \frac{\pi}{180} = \frac{45\pi}{180} = \frac{\pi}{4} $ рад</p><p>$ 60^{\circ} = 60 \cdot \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3} $ рад</p><p><strong>Ответ:</strong> $ \frac{\pi}{10} $, $ \frac{3\pi}{20} $, $ \frac{\pi}{6} $, $ \frac{\pi}{4} $, $ \frac{\pi}{3} $.</p><p><strong>б)</strong></p><p>$ 90^{\circ} = 90 \cdot \frac{\pi}{180} = \frac{90\pi}{180} = \frac{\pi}{2} $ рад</p><p>$ 120^{\circ} = 120 \cdot \frac{\pi}{180} = \frac{120\pi}{180} = \frac{2\pi}{3} $ рад (сокращаем на 60)</p><p>$ 135^{\circ} = 135 \cdot \frac{\pi}{180} = \frac{135\pi}{180} = \frac{3\pi}{4} $ рад (сокращаем на 45)</p><p>$ 150^{\circ} = 150 \cdot \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6} $ рад (сокращаем на 30)</p><p><strong>Ответ:</strong> $ \frac{\pi}{2} $, $ \frac{2\pi}{3} $, $ \frac{3\pi}{4} $, $ \frac{5\pi}{6} $.</p><p><strong>в)</strong></p><p>$ 210^{\circ} = 210 \cdot \frac{\pi}{180} = \frac{210\pi}{180} = \frac{7\pi}{6} $ рад (сокращаем на 30)</p><p>$ 225^{\circ} = 225 \cdot \frac{\pi}{180} = \frac{225\pi}{180} = \frac{5\pi}{4} $ рад (сокращаем на 45)</p><p>$ 270^{\circ} = 270 \cdot \frac{\pi}{180} = \frac{270\pi}{180} = \frac{3\pi}{2} $ рад (сокращаем на 90)</p><p>$ 300^{\circ} = 300 \cdot \frac{\pi}{180} = \frac{300\pi}{180} = \frac{5\pi}{3} $ рад (сокращаем на 60)</p><p><strong>Ответ:</strong> $ \frac{7\pi}{6} $, $ \frac{5\pi}{4} $, $ \frac{3\pi}{2} $, $ \frac{5\pi}{3} $.</p><p><strong>г)</strong></p><p>$ 1100^{\circ} = 1100 \cdot \frac{\pi}{180} = \frac{1100\pi}{180} = \frac{110\pi}{18} = \frac{55\pi}{9} $ рад (сокращаем на 20)</p><p>$ 1440^{\circ} = 1440 \cdot \frac{\pi}{180} = \frac{1440\pi}{180} = \frac{144\pi}{18} = 8\pi $ рад (сокращаем на 180)</p><p>$ 3330^{\circ} = 3330 \cdot \frac{\pi}{180} = \frac{3330\pi}{180} = \frac{333\pi}{18} = \frac{37\pi}{2} $ рад (сокращаем на 90)</p><p>$ 7380^{\circ} = 7380 \cdot \frac{\pi}{180} = \frac{7380\pi}{180} = \frac{738\pi}{18} = 41\pi $ рад (сокращаем на 180)</p><p><strong>Ответ:</strong> $ \frac{55\pi}{9} $, $ 8\pi $, $ \frac{37\pi}{2} $, $ 41\pi $.</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" => "1108255" "type" => "task" ] "previous" => array:2 [ "refs" => "1108253" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\BookPage {#1039 #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" => 1097896 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-154" "field_display_title" => "154" "field_folder" => "folder1" "field_image_name" => "154" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1048} ] #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 {#1112 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Element {#1126 #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" => 1261047 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1261047 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128} "book_page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #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" => "1097897" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097895" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:8 [ 0 => App\Models\Task {#1210 #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" => 1108251 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-521" "field_display_title" => "521" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ …1] #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 {#1212 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108252" "type" => "task" ] "previous" => array:2 [ "refs" => "1108250" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108251 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-521" "field_display_title" => "521" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1211} "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 {#1212} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1213} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1214} "content" => Illuminate\Database\Eloquent\Collection {#1217} "next" => array:2 [ "refs" => "1108252" "type" => "task" ] "previous" => array:2 [ "refs" => "1108250" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #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 {#1216 #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" => 1108252 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-522" "field_display_title" => "522" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1215 #items: array:1 [ …1] #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 {#1222 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108253" "type" => "task" ] "previous" => array:2 [ "refs" => "1108251" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108252 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-522" "field_display_title" => "522" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1215} "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 {#1222} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1224} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1220} "content" => Illuminate\Database\Eloquent\Collection {#1219} "next" => array:2 [ "refs" => "1108253" "type" => "task" ] "previous" => array:2 [ "refs" => "1108251" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1237} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #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\Task {#1221 #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" => 1108253 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-523" "field_display_title" => "523" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:1 [ …1] #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 {#1236 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1238 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108254" "type" => "task" ] "previous" => array:2 [ "refs" => "1108252" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108253 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-523" "field_display_title" => "523" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1218} "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 {#1236} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1238} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1234} "content" => Illuminate\Database\Eloquent\Collection {#1233} "next" => array:2 [ "refs" => "1108254" "type" => "task" ] "previous" => array:2 [ "refs" => "1108252" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1251} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1235 #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" => 1108254 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-524" "field_display_title" => "524" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:1 [ …1] #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 {#1250 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1252 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108255" "type" => "task" ] "previous" => array:2 [ "refs" => "1108253" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108254 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-524" "field_display_title" => "524" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1232} "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 {#1250} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1252} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248} "content" => Illuminate\Database\Eloquent\Collection {#1246} "next" => array:2 [ "refs" => "1108255" "type" => "task" ] "previous" => array:2 [ "refs" => "1108253" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1249} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1247 #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" => 1108255 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-525" "field_display_title" => "525" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:1 [ …1] #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 {#1261 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1262 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108256" "type" => "task" ] "previous" => array:2 [ "refs" => "1108254" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1272 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108255 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-525" "field_display_title" => "525" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260} "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 {#1261} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1262} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263} "content" => Illuminate\Database\Eloquent\Collection {#1266} "next" => array:2 [ "refs" => "1108256" "type" => "task" ] "previous" => array:2 [ "refs" => "1108254" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1272} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1265 #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" => 1108256 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-526" "field_display_title" => "526" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:1 [ …1] #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 {#1271 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1268 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108257" "type" => "task" ] "previous" => array:2 [ "refs" => "1108255" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108256 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-526" "field_display_title" => "526" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264} "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 {#1271} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1273} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1269} "content" => Illuminate\Database\Eloquent\Collection {#1268} "next" => array:2 [ "refs" => "1108257" "type" => "task" ] "previous" => array:2 [ "refs" => "1108255" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1270 #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" => 1108257 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-527" "field_display_title" => "527" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ …1] #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 {#1285 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1283 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1282 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108258" "type" => "task" ] "previous" => array:2 [ "refs" => "1108256" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #original: array:24 [ "id" => 1108257 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-527" "field_display_title" => "527" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267} "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 {#1285} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1287} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1283} "content" => Illuminate\Database\Eloquent\Collection {#1282} "next" => array:2 [ "refs" => "1108258" "type" => "task" ] "previous" => array:2 [ "refs" => "1108256" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1300} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 7 => App\Models\Task {#1284 #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" => 1108258 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-528" "field_display_title" => "528" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1281 #items: array:1 [ …1] #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 {#1299 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108259" "type" => "task" ] "previous" => array:2 [ "refs" => "1108257" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1314 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108258 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-528" "field_display_title" => "528" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1281} "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 {#1299} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297} "content" => Illuminate\Database\Eloquent\Collection {#1296} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1314 …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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1097896 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-154" "field_display_title" => "154" "field_folder" => "folder1" "field_image_name" => "154" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1042} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1103} "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 {#1112} "content" => Illuminate\Database\Eloquent\Collection {#1127} "next" => array:2 [ "refs" => "1097897" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097895" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1196} ] #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" => 1108254 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "154" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-524" "field_display_title" => "524" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "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 {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1105} "content" => Illuminate\Database\Eloquent\Collection {#1102} "next" => array:2 [ "refs" => "1108255" "type" => "task" ] "previous" => array:2 [ "refs" => "1108253" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1098} "page" => array:2 [ "refs" => "1097896" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№524 (с. 154)
Условие. №524 (с. 154)
скриншот условия
524. Найдите радианную меру угла поворота, заданного в градусах:
а) $18^\circ$, $27^\circ$, $30^\circ$, $45^\circ$, $60^\circ$;
б) $90^\circ$, $120^\circ$, $135^\circ$, $150^\circ$;
в) $210^\circ$, $225^\circ$, $270^\circ$, $300^\circ$;
г) $1100^\circ$, $1440^\circ$, $3330^\circ$, $7380^\circ$.
Решение. №524 (с. 154)
Решение 2 (rus). №524 (с. 154)
Для перевода градусной меры угла в радианную используется формула, связывающая градусы и радианы, исходя из того, что $180^{\circ}$ равны $ \pi $ радиан:
$ \alpha_{рад} = \alpha_{град} \cdot \frac{\pi}{180^{\circ}} $
Где $ \alpha_{рад} $ — мера угла в радианах, а $ \alpha_{град} $ — мера угла в градусах.
а)
$ 18^{\circ} = 18 \cdot \frac{\pi}{180} = \frac{18\pi}{180} = \frac{\pi}{10} $ рад
$ 27^{\circ} = 27 \cdot \frac{\pi}{180} = \frac{27\pi}{180} = \frac{3\pi}{20} $ рад (сокращаем на 9)
$ 30^{\circ} = 30 \cdot \frac{\pi}{180} = \frac{30\pi}{180} = \frac{\pi}{6} $ рад
$ 45^{\circ} = 45 \cdot \frac{\pi}{180} = \frac{45\pi}{180} = \frac{\pi}{4} $ рад
$ 60^{\circ} = 60 \cdot \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3} $ рад
Ответ: $ \frac{\pi}{10} $, $ \frac{3\pi}{20} $, $ \frac{\pi}{6} $, $ \frac{\pi}{4} $, $ \frac{\pi}{3} $.
б)
$ 90^{\circ} = 90 \cdot \frac{\pi}{180} = \frac{90\pi}{180} = \frac{\pi}{2} $ рад
$ 120^{\circ} = 120 \cdot \frac{\pi}{180} = \frac{120\pi}{180} = \frac{2\pi}{3} $ рад (сокращаем на 60)
$ 135^{\circ} = 135 \cdot \frac{\pi}{180} = \frac{135\pi}{180} = \frac{3\pi}{4} $ рад (сокращаем на 45)
$ 150^{\circ} = 150 \cdot \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6} $ рад (сокращаем на 30)
Ответ: $ \frac{\pi}{2} $, $ \frac{2\pi}{3} $, $ \frac{3\pi}{4} $, $ \frac{5\pi}{6} $.
в)
$ 210^{\circ} = 210 \cdot \frac{\pi}{180} = \frac{210\pi}{180} = \frac{7\pi}{6} $ рад (сокращаем на 30)
$ 225^{\circ} = 225 \cdot \frac{\pi}{180} = \frac{225\pi}{180} = \frac{5\pi}{4} $ рад (сокращаем на 45)
$ 270^{\circ} = 270 \cdot \frac{\pi}{180} = \frac{270\pi}{180} = \frac{3\pi}{2} $ рад (сокращаем на 90)
$ 300^{\circ} = 300 \cdot \frac{\pi}{180} = \frac{300\pi}{180} = \frac{5\pi}{3} $ рад (сокращаем на 60)
Ответ: $ \frac{7\pi}{6} $, $ \frac{5\pi}{4} $, $ \frac{3\pi}{2} $, $ \frac{5\pi}{3} $.
г)
$ 1100^{\circ} = 1100 \cdot \frac{\pi}{180} = \frac{1100\pi}{180} = \frac{110\pi}{18} = \frac{55\pi}{9} $ рад (сокращаем на 20)
$ 1440^{\circ} = 1440 \cdot \frac{\pi}{180} = \frac{1440\pi}{180} = \frac{144\pi}{18} = 8\pi $ рад (сокращаем на 180)
$ 3330^{\circ} = 3330 \cdot \frac{\pi}{180} = \frac{3330\pi}{180} = \frac{333\pi}{18} = \frac{37\pi}{2} $ рад (сокращаем на 90)
$ 7380^{\circ} = 7380 \cdot \frac{\pi}{180} = \frac{7380\pi}{180} = \frac{738\pi}{18} = 41\pi $ рад (сокращаем на 180)
Ответ: $ \frac{55\pi}{9} $, $ 8\pi $, $ \frac{37\pi}{2} $, $ 41\pi $.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по алгебре за 9 класс, для упражнения номер 524 расположенного на странице 154 к учебнику 2019 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по алгебре к упражнению №524 (с. 154), авторов: Солтан (Генадий Николаевич), Солтан (Алла Евгеньевна), Жумадилова (Аманбала Жумадиловна), учебного пособия издательства Кокшетау.