{"id":34930,"date":"2024-03-03T11:49:31","date_gmt":"2024-03-03T11:49:31","guid":{"rendered":"https:\/\/umschool.net\/library\/?p=34930"},"modified":"2024-03-03T11:52:13","modified_gmt":"2024-03-03T11:52:13","slug":"trigonometricheskie-podstanovki","status":"publish","type":"post","link":"https:\/\/umschool.net\/library\/matematika\/trigonometricheskie-podstanovki\/","title":{"rendered":"\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438"},"content":{"rendered":"\n<h3 class=\"has-text-align-center wp-block-heading\"><strong>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>\u041f\u043e\u0447\u0435\u043c\u0443 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438\u043c\u0435\u043d\u043d\u043e \u0442\u0430\u043a?<\/li><li>\u041a\u0430\u043a \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0437\u0430 \u0440\u0443\u0431\u0435\u0436\u043e\u043c?&nbsp;<\/li><li>\u041a\u0430\u043a \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u043f\u0440\u0435\u0432\u0440\u0430\u0442\u0438\u0442\u044c \u0432 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0439?<\/li><\/ul>\n\n\n\n<p>\u0411\u044b\u0432\u0430\u043b\u043e \u0443 \u0432\u0430\u0441 \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e \u0440\u0435\u0448\u0430\u0435\u0442\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043d\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u0432\u0430\u043c \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u043d\u0435 \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442? \u0421\u043a\u043e\u0440\u0435\u0435 \u0432\u0441\u0435\u0433\u043e, \u0432 \u044d\u0442\u043e\u0439 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438 \u0432\u0430\u043c \u043f\u043e\u043c\u043e\u0433\u0443\u0442 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0438 \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e.&nbsp;<\/p>\n\n\n\n<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0438 \u0443\u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0438 \u043a\u0430\u043a \u043e\u043d\u0438 \u043f\u043e\u043c\u043e\u0433\u0443\u0442 \u043d\u0430\u043c \u043d\u0430 \u0415\u0413\u042d.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435-\u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438<\/h2>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f <\/strong>\u2014 \u0440\u0430\u0437\u0434\u0435\u043b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0438\u0437\u0443\u0447\u0430\u044e\u0442\u0441\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u0443\u0433\u043b\u0430\u043c\u0438 \u0438 \u0441\u0442\u043e\u0440\u043e\u043d\u0430\u043c\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n\n\n\n<p>\u041f\u0435\u0440\u0435\u0434 \u0442\u0435\u043c, \u043a\u0430\u043a \u043d\u0430\u0447\u043d\u0435\u043c, \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043c \u043e\u0441\u043d\u043e\u0432\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u0440\u043e\u0447\u0438\u0442\u0430\u0442\u044c \u044d\u0442\u0438 \u0441\u0442\u0430\u0442\u044c\u0438:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/umschool.net\/library\/matematika\/trigonometricheskaya-okruzhnost-chast-1\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c. \u0427\u0430\u0441\u0442\u044c 1<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/trigonometricheskaya-okruzhnost-chast-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c. \u0427\u0430\u0441\u0442\u044c 2<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/grafiki-trigonometricheskih-funkczij\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0413\u0440\u0430\u0444\u0438\u043a\u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/formuly-trigonometrii-i-prostejshie-uravneniya\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0438 \u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/formuly-privedeniya\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u0438\u044f<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/trigonometricheskie-uravneniya\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/a><\/li><li><a href=\"https:\/\/umschool.net\/library\/matematika\/trigonometricheskie-neravenstva\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430<\/a><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u041f\u043e\u0447\u0435\u043c\u0443 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438\u043c\u0435\u043d\u043d\u043e \u0442\u0430\u043a?<\/strong><br><br>\u0421\u043b\u043e\u0432\u043e \u00ab\u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f\u00bb \u043f\u0440\u043e\u0438\u0437\u043e\u0448\u043b\u043e \u0438\u0437 \u043b\u0430\u0442\u044b\u043d\u0438, \u0438 \u043e\u043d\u043e \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0441\u043b\u043e\u0432: trig\u014dnon \u2014 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a, metre\u014d \u2014 \u0438\u0437\u043c\u0435\u0440\u044f\u0442\u044c.\u00a0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/1-pravka-1024x389.png\" alt=\"\" class=\"wp-image-34934\" width=\"512\" height=\"195\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/1-pravka-1024x389.png 1024w, \/library\/wp-content\/uploads\/2024\/03\/1-pravka-300x114.png 300w, \/library\/wp-content\/uploads\/2024\/03\/1-pravka-768x292.png 768w, \/library\/wp-content\/uploads\/2024\/03\/1-pravka-1536x584.png 1536w, \/library\/wp-content\/uploads\/2024\/03\/1-pravka.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p>\u041f\u043e\u0440\u043e\u0439 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043a\u0430\u0436\u0443\u0442\u0441\u044f \u0441\u043b\u043e\u0436\u043d\u044b\u043c\u0438 \u0438 \u043d\u0435\u043f\u043e\u043d\u044f\u0442\u043d\u044b\u043c\u0438. \u041d\u043e \u0435\u0441\u0442\u044c \u0441\u043f\u043e\u0441\u043e\u0431 \u0438\u0445 \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>\u041a\u0430\u043a \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0437\u0430 \u0440\u0443\u0431\u0435\u0436\u043e\u043c?<\/strong><br><br>\u0412 \u0430\u043d\u0433\u043b\u0438\u0439\u0441\u043a\u043e\u0439 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0435 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u043e\u0439 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430, \u0432 \u0447\u0435\u0441\u0442\u044c \u041a\u0430\u0440\u043b\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430, \u043d\u0435\u043c\u0435\u0446\u043a\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438, \u043a\u0430\u043a \u043f\u0440\u043e \u043d\u0435\u0433\u043e \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u00ab\u043e\u0442\u0446\u0430 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0438\u0437\u0430\u00bb. \u041e\u043d \u0432\u044b\u0432\u0435\u043b \u044d\u0442\u0443 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0443 \u0432 \u0441\u0432\u043e\u0438\u0445 \u0442\u0440\u0443\u0434\u0430\u0445 \u0432 1860-\u0445 \u0433\u043e\u0434\u0430\u0445.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430<\/strong> \u2014 \u0447\u0430\u0441\u0442\u043d\u044b\u0439 \u0441\u043b\u0443\u0447\u0430\u0439 \u0437\u0430\u043c\u0435\u043d\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0434\u0432\u043e\u0439\u043d\u043e\u0433\u043e \u0443\u0433\u043b\u0430.&nbsp;<\/p>\n\n\n\n<p>\u0427\u0430\u0449\u0435 \u0432\u0441\u0435\u0433\u043e \u0438\u0445 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442 \u0432 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438, \u043d\u043e \u043c\u044b \u0438\u0445 \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u0438\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439.&nbsp;<\/p>\n\n\n\n<p>\u0414\u043b\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043e\u043a \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0441\u0432\u043e\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0443\u0447\u0438\u0442\u044c. \u041e\u0434\u043d\u0430\u043a\u043e \u043c\u044b \u043f\u043e\u0439\u0434\u0435\u043c \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0434\u0440\u0443\u0433\u0438\u043c \u043f\u0443\u0442\u0435\u043c \u0438 \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u0438\u0445 \u0441\u0430\u043c\u0438! \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u044b\u0435 \u0432 \u0442\u0430\u0431\u043b\u0438\u0446\u0430\u0445 \u043d\u0438\u0436\u0435.&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image.png\" alt=\"\" class=\"wp-image-34935\" width=\"576\" height=\"707\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image.png 768w, \/library\/wp-content\/uploads\/2024\/03\/image-245x300.png 245w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-1.png\" alt=\"\" class=\"wp-image-34936\" width=\"576\" height=\"473\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-1.png 768w, \/library\/wp-content\/uploads\/2024\/03\/image-1-300x246.png 300w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u0412\u044b\u0432\u0435\u0434\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u0441\u0438\u043d\u0443\u0441\u0430:<\/strong><\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\">\\(sin(x) = sin(2*\\frac{x}{2})\\)<\/p>\n\n\n\n<p>\u0423 \u043d\u0430\u0441 \u043f\u043e\u044f\u0432\u0438\u043b\u0430\u0441\u044c \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u0432\u043e\u0439\u043d\u043e\u0433\u043e \u0443\u0433\u043b\u0430:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(sin(2*\\frac{x}{2}) = 2sin(\\frac{x}{2})*cos(\\frac{x}{2})\\)<\/p>\n\n\n\n<p>\u0412 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \u0440\u0430\u0441\u043f\u0438\u0448\u0435\u043c \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043e, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0440\u0430\u0432\u043d\u043e \u0435\u0434\u0438\u043d\u0438\u0446\u0435:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{2sin(\\frac{x}{2})*cos(\\frac{x}{2})}{1}=\\frac{2sin(\\frac{x}{2})*cos(\\frac{x}{2})}{cos^2(\\frac{x}{2})+sin2(\\frac{x}{2})}\\)<\/p>\n\n\n\n<p>\u0422\u0435\u043f\u0435\u0440\u044c, \u0435\u0441\u043b\u0438 \u043c\u044b \u0438 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c, \u0438 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043f\u043e\u0434\u0435\u043b\u0438\u043c \u043d\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435, \u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{\\frac{2sin(\\frac{x}{2})*cos(\\frac{x}{2})}{cos^2(\\frac{x}{2})}}{\\frac{cos^2(\\frac{x}{2})+sin^2(\\frac{x}{2})}{cos^2(\\frac{x}{2})}}=\\frac{\\frac{2sin(\\frac{x}{2})}{cos(\\frac{x}{2})}}{\\frac{cos^2(\\frac{x}{2})}{cos^2(\\frac{x}{2})}+\\frac{sin^2(\\frac{x}{2})}{cos^2(\\frac{x}{2})}}=\\frac{2tg(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<\/p>\n\n\n\n<p>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0442\u0430\u043a\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u0441\u0438\u043d\u0443\u0441\u0430:<\/p>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#f0e5ff\">\\(sin(x) =\\frac{2tg(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430:<\/strong><\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\">\\(cos(x)=cos(2\\frac{x}{2})=\\frac{cos^2(\\frac{x}{2})-sin^2(\\frac{x}{2})}{cos^2(\\frac{x}{2})+sin^2(\\frac{x}{2})}=\\frac{1-tg^2(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<\/p>\n\n\n\n<p>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430:<\/p>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#f0e5ff\">\\(cos(x) =\\frac{1-tg^2(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u0422\u0430\u043d\u0433\u0435\u043d\u0441<\/strong> \u0440\u0430\u0432\u0435\u043d \u0441\u0438\u043d\u0443\u0441\u0443 \u043f\u043e\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441, \u043f\u043e\u044d\u0442\u043e\u043c\u0443:<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\">\\(tg(x)=\\frac{2tg(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})} :\\frac{1-tg^2(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}=\\frac{2tg(\\frac{x}{2})*(1+tg^2(\\frac{x}{2}))}{(1+tg^2(\\frac{x}{2}))*(1-tg^2(\\frac{x}{2}))}\\)<\/p>\n\n\n\n<p>\\((1+tg^2(\\frac{x}{2}))\\) \u0441\u043e\u043a\u0440\u0430\u0442\u0438\u0442\u0441\u044f, \u0438 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0442\u0430\u043a\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430:<\/p>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#f0e5ff\">\\(tg(x)=\\frac{2tg(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0410 \u0442\u0430\u043a \u043a\u0430\u043a <strong>\u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441<\/strong> \u043e\u0431\u0440\u0430\u0442\u0435\u043d \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0443 \\((ctg(x)=\\frac{1}{tg(x)})\\), \u0442\u043e \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a:<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#f0e5ff\">\\(ctg(x)=\\frac{1-tg^2(\\frac{x}{2})}{2tg(\\frac{x}{2})}\\)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/photo1691152501-417x1024.jpeg\" alt=\"\" class=\"wp-image-34958\" width=\"20\" height=\"49\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/photo1691152501-417x1024.jpeg 417w, \/library\/wp-content\/uploads\/2024\/03\/photo1691152501-122x300.jpeg 122w, \/library\/wp-content\/uploads\/2024\/03\/photo1691152501.jpeg 521w\" sizes=\"auto, (max-width: 20px) 100vw, 20px\" \/><\/figure><\/div>\n\n\n\n<p>\u0412\u0430\u0436\u043d\u043e \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u0437\u0430\u043c\u0435\u043d\u0430 \u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0432\u0435\u0434\u0435\u0442 \u043a \u0441\u0443\u0436\u0435\u043d\u0438\u044e \u041e\u0414\u0417, \u0442\u0430\u043a \u043a\u0430\u043a \u0438\u0441\u043a\u043b\u044e\u0447\u0430\u044e\u0442\u0441\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <em>x<\/em>, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \\(cos(\\frac{x}{2})=0\\), \u0442\u043e \u0435\u0441\u0442\u044c \\(x=\\pi+2\\pi n, n\\in Z\\).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u041a\u0430\u043a \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u043f\u0440\u0435\u0432\u0440\u0430\u0442\u0438\u0442\u044c \u0432 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0439?<\/strong><br><br>\u0414\u043b\u044f \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0432\u044b\u0433\u043b\u044f\u0434\u0435\u043b\u0438 \u043f\u0440\u043e\u0449\u0435, \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0437\u0430\u043c\u0435\u043d\u0443 \\(tg(\\frac{x}{2})=t\\), \u0438 \u0442\u043e\u0433\u0434\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0431\u0443\u0434\u0443\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0438:<br><br>\\(sin(x)=\\frac{2t}{1+t^2}\\)<br>\\(cos(x) =\\frac{1-t^2}{1+t^2}\\)<br>\\(tg(x)=\\frac{2t}{1-t^2}\\)<br>\\(ctg(x)=\\frac{1-t^2}{2t}\\)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-2-969x1024.png\" alt=\"\" class=\"wp-image-34962\" width=\"485\" height=\"512\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-2-969x1024.png 969w, \/library\/wp-content\/uploads\/2024\/03\/image-2-284x300.png 284w, \/library\/wp-content\/uploads\/2024\/03\/image-2-768x812.png 768w, \/library\/wp-content\/uploads\/2024\/03\/image-2-1453x1536.png 1453w, \/library\/wp-content\/uploads\/2024\/03\/image-2.png 1514w\" sizes=\"auto, (max-width: 485px) 100vw, 485px\" \/><\/figure><\/div>\n\n\n\n<p>\u0418\u0442\u0430\u043a, \u043e\u0431\u043e\u0431\u0449\u0438\u043c \u0432\u0441\u0435, \u0447\u0442\u043e \u0438\u0437\u0443\u0447\u0438\u043b\u0438:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0415\u0435 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0441 \u0437\u0430\u043c\u0435\u043d\u043e\u0439<\/strong><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\\(sin(x)\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{2tg(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{2t}{1+t^2}\\)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\\(cos(x)\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{1-tg2(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{1-t^2}{1+t^2}\\)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\\(tg(x)\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{2tg(\\frac{x}{2})}{1-tg^2(\\frac{x}{2})}\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{2t}{1-t^2}\\)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\\(ctg(x)\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{1-tg^2(\\frac{x}{2})}{2tg(\\frac{x}{2})}\\)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{1-t^2}{2t}\\)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2024\/03\/image-3-1024x982.png\" alt=\"\" class=\"wp-image-34963\" width=\"512\" height=\"491\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-3-1024x982.png 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-3-300x288.png 300w, \/library\/wp-content\/uploads\/2024\/03\/image-3-768x737.png 768w, \/library\/wp-content\/uploads\/2024\/03\/image-3-1536x1473.png 1536w, \/library\/wp-content\/uploads\/2024\/03\/image-3.png 1539w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u043e\u0431\u0443\u0435\u043c \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435.<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\">\u0420\u0435\u0448\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430<strong> \u0415\u0413\u042d \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0432 \u0437\u0430\u0434\u0430\u043d\u0438\u0438 \u211613, \u043f\u0443\u043d\u043a\u0442 \u0430.<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0430) \u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <\/em>\\(sin(2x)+tgx=-2\\).<br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u041f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0443:<br><br>\\(sin(2x) =\\frac{2tg(x)}{1+tg^2(x)}\\)<br><br>\u041f\u043e\u043b\u0443\u0447\u0438\u043c:<br>\\(\\frac{2tg(x)}{1+tg^2(x)}+tg(x)=-2\\)<br><br>\u0421\u0434\u0435\u043b\u0430\u0435\u043c \u0437\u0430\u043c\u0435\u043d\u0443 \\(t=tg(x)\\):<br>\\(\\frac{2t}{1+t^2}+t=-2\\)<br><br>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \\(-2\\) \u0432 \u043b\u0435\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c \u0438 \u0437\u0430\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u043f\u043e\u0434 \u043e\u0434\u0438\u043d \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c:<br><br>\\(\\frac{2t+t+t^3+2+2t^2}{1+t^2}=0\\)<br><br>\u0414\u043e\u043c\u043d\u043e\u0436\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \\(1+t^2\\), \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 \u0434\u0440\u043e\u0431\u0435\u0439. \u041c\u044b \u044d\u0442\u043e \u043c\u043e\u0436\u0435\u043c \u0441\u0434\u0435\u043b\u0430\u0442\u044c, \u0442\u0430\u043a \u043a\u0430\u043a \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e \u043f\u0440\u0438 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u043a\u043e\u0440\u043d\u044f\u0445. <br><br>\u041f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435:<br>\\(t^3+2t^2+3t+2=0\\)<br><br>\u041f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<br><br>\\(t^2(t+1)+t(t+1)+2(t+1)=0\\)<br>\\((t+1)(t^2+t+2)=0\\)<br><br>\u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e, \u0442\u043e \u043a\u0430\u043a \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u043e\u0434\u0438\u043d \u0438\u0437 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0435\u0439 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e.\u00a0<br>&#8212; \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0435\u0440\u0432\u044b\u0439:<br>\\(t+1=0\\)<br>\\(t=-1\\)<br>&#8212; \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u0442\u043e\u0440\u043e\u0439:<br>\\(t^2+t+2=0\\)<br>\\(D=1-8=-7\\)<br><br>\u0414\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \u043c\u0435\u043d\u044c\u0448\u0435 \u043d\u0443\u043b\u044f, \u0437\u043d\u0430\u0447\u0438\u0442 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u043a\u043e\u0440\u043d\u0435\u0439 \u043d\u0435\u0442.<br><br>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f, \\(t=-1\\) \u0438\u043b\u0438, \u0434\u0435\u043b\u0430\u044f \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u0437\u0430\u043c\u0435\u043d\u0443, \\(tg(x)=-1\\). \u0420\u0435\u0448\u0438\u043c \u044d\u0442\u043e:<br><br>\\(tg(x)=-1\\)<br>\\(x=\\frac{3\\pi}{4}+\\pi k, k\\in Z\\)<br><br>\u042d\u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \\(x\\) \u0432\u0445\u043e\u0434\u0438\u0442 \u0432 \u041e\u0414\u0417 \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \u2014 \\(x\\neq \\frac{\\pi}{2}+\\pi k, k\\in Z\\). \u041f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043e\u0442\u0432\u0435\u0442.<br><br><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\\(x=\\frac{3\\pi}{4}+\\pi k, k\\in Z\\).<\/p>\n\n\n\n<p>\u0420\u0430\u0437\u0431\u0435\u0440\u0435\u043c \u0435\u0449\u0435 \u043e\u0434\u043d\u0443 \u0437\u0430\u0434\u0430\u0447\u0443 \u0438\u0437 \u0415\u0413\u042d.<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\">\u0420\u0435\u0448\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430<strong> \u0415\u0413\u042d \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0432 \u0437\u0430\u0434\u0430\u043d\u0438\u0438 \u211613, \u043f\u0443\u043d\u043a\u0442 \u0430.<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0430) \u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <\/em>\\(12+12cos(x)+10sin(x)cos(x)=0\\).<br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u041f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0443 \u0438 \u0441\u0434\u0435\u043b\u0430\u0435\u043c \u0437\u0430\u043c\u0435\u043d\u0443 \\(t=tg(\\frac{x}{2})\\):<br><br>\\(12+121-t21+t2+20t(1-t2)(1+t2)2=0\\)<br><br>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<br>\\(\\frac{12(1+t^2)^2+12(1+t^2)(1-t^2)+20t(1-t^2)}{(1+t^2)^2}=0\\)<br>\\(\\frac{12(1+2t^2+t^4)+12(1-t^4)+20t(1-t^2)}{(1+t^2)^2}=0\\)<br>\\(\\frac{12+24t^2+12t^4+12-12t^4+20t-20t^3}{(1+t^2)^2}=0\\)<br><br>\u0414\u043e\u043c\u043d\u043e\u0436\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \\((1+t^2)^2\\):<br>\\(-20t^3+24t^2+20t+24=0\\)<br><br>\u041f\u043e\u0434\u0435\u043b\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \\(-4\\):<br>\\(5t^3-6t^2-5t+6=0\\)<br><br>\u0412\u044b\u043d\u0435\u0441\u0435\u043c \\((t-2)\\):<br>\\((t-2)(5t^2+4t+3)=0\\)<br><br>\u041f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e, \u043a\u043e\u0433\u0434\u0430 \u043e\u0434\u0438\u043d \u0438\u0437 \u0435\u0433\u043e \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0435\u0439 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u043d\u043e \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u044c \\(5t^2+4t+3\\) \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e. <br><br>\u0422\u043e\u0433\u0434\u0430 \u0438\u043c\u0435\u0435\u043c:<br>\\(t-2=0\\)<br>\\(t=2\\)<br><br>\u0417\u043d\u0430\u0447\u0438\u0442, \\(tg(\\frac{x}{2})=2\\) \u0438 \\(x=2arctg(2)+2\\pi k, k\\in Z\\).<br><br>\u041a\u0430\u0437\u0430\u043b\u043e\u0441\u044c \u0431\u044b, \u0447\u0442\u043e \u043c\u044b \u0440\u0435\u0448\u0438\u043b\u0438 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043d\u043e \u043d\u0435 \u0442\u0443\u0442-\u0442\u043e \u0431\u044b\u043b\u043e. \u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u0434\u0435\u043b\u0430\u043b\u0438 \u0437\u0430\u043c\u0435\u043d\u0443, \u0438\u0437 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u043f\u0430\u043b \u043a\u043e\u0440\u0435\u043d\u044c \\(cos(x2)=0\\), \u0442\u043e \u0435\u0441\u0442\u044c \\(x=+2n, n Z\\). \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u0435\u0433\u043e \u0432 \u043f\u0435\u0440\u0432\u043e\u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u043c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d \u0435\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c:<br><br>\\(12+12cos()+10sin(x)cos()=0\\)<br>\\(12-12-10sin(x)=0\\)<br>\\(-10sin(x)=0\\)<br>\\(10sin(x)=0\\)<br>\\(sin(x)=0\\)<br><br>\u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0435\u0441\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435, \u0438 \u043e\u043d\u043e:<br>\\(x=k, k Z\\).<br><br>\u0417\u043d\u0430\u0447\u0438\u0442, \\(x=+2n, n Z\\) \u0442\u043e\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<br><br><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\\(x1=+2k, x2=2arctg(2)+2k, k Z\\)<\/p>\n\n\n\n<p>\u0421\u0435\u0433\u043e\u0434\u043d\u044f \u043c\u044b \u0443\u0437\u043d\u0430\u043b\u0438, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0438 \u043a\u0430\u043a \u0435\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435. \u0412 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0440\u0430\u0437 \u043c\u044b \u0440\u0430\u0437\u0431\u0435\u0440\u0435\u043c, \u043a\u0430\u043a <a href=\"https:\/\/umschool.net\/library\/matematika\/reshenie-zadach-s-parametrom-metodom-issledovatelskogo-analiza\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0438\u0437\u0430<\/a>.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0424\u0430\u043a\u0442\u0447\u0435\u043a<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u044b\u0432\u0430\u0442\u044c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0438\u0437 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0435.\u00a0<\/li><li>\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043e\u043a:<br>\\(sin(x) =\\frac{2tg(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<br>\\(cos(x) =\\frac{1-tg^2(\\frac{x}{2})}{1+tg^2(\\frac{x}{2})}\\)<br>\\(tg(x)=\\frac{2tg(\\frac{x}{2})}{1-tg^2(\\frac{x}{2})}\\)<br>\\(ctg(x)=\\frac{1-tg^2(\\frac{x}{2})}{2tg(\\frac{x}{2})}\\)<\/li><li>\u0427\u0442\u043e\u0431\u044b \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0434\u0440\u043e\u0431\u044c \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u0438\u044f\u0442\u043d\u043e\u0439 \u043d\u0430 \u0432\u0438\u0434, \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0437\u0430\u043c\u0435\u043d\u0443 \\(tg(\\frac{x}{2})=t\\).<\/li><\/ul>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u041f\u0440\u043e\u0432\u0435\u0440\u044c \u0441\u0435\u0431\u044f<\/strong><\/h2>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 1.<\/strong><br>\u0412 \u043a\u0430\u043a\u043e\u043c \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0435 \u043e\u0442\u0432\u0435\u0442\u0430 \u043d\u0430\u043f\u0438\u0441\u0430\u043d \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0439 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0434\u043b\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(1-t^2\\)<\/li><li>\\(2t\\)<\/li><li>\\(1+t^2\\)<\/li><li>\\(t\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 2.<\/strong><br>\u041a\u0430\u043a \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0434\u043b\u044f \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(1+t^2\\)<\/li><li>\\(t^2\\)<\/li><li>\\(1-t^2\\)<\/li><li>\\(2t\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 3.<\/strong><br>\u041a\u0430\u043a\u0430\u044f \u0437\u0430\u043c\u0435\u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(cos(\\frac{x}{2})=t\\)<\/li><li>\\(ctg(\\frac{x}{2})=t\\)<\/li><li>\\(tg(\\frac{x}{2})=t\\)<\/li><li>\\(sin(\\frac{x}{2})=t\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 4.<\/strong><br>\u041a\u0430\u043a \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(ctg(x)\\) \u0441 \u0437\u0430\u043c\u0435\u043d\u043e\u0439?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(\\frac{2t}{1-t^2}\\)<\/li><li>\\(\\frac{1-t^2}{2t}\\)<\/li><li>\\(\\frac{2t}{1+t^2}\\)<\/li><li>\\(\\frac{1-tg^2(\\frac{x}{2})}{2tg(\\frac{x}{2})}\\)<\/li><\/ol>\n\n\n\n<p><strong>\u041e\u0442\u0432\u0435\u0442\u044b: 1. \u2014 <\/strong>1;<strong> 2. \u2014 <\/strong>3;<strong> 3. \u2014 <\/strong>4;<strong> 4. \u2014 <\/strong>2.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u041f\u043e\u0447\u0435\u043c\u0443 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438\u043c\u0435\u043d\u043d\u043e \u0442\u0430\u043a? \u041a\u0430\u043a \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u0437\u0430 \u0440\u0443\u0431\u0435\u0436\u043e\u043c?&nbsp; \u041a\u0430\u043a \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u043f\u0440\u0435\u0432\u0440\u0430\u0442\u0438\u0442\u044c \u0432 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0439? \u0411\u044b\u0432\u0430\u043b\u043e \u0443 \u0432\u0430\u0441 \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e \u0440\u0435\u0448\u0430\u0435\u0442\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043d\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u0432\u0430\u043c \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u043d\u0435 \u043f\u043e\u043c\u043e\u0433\u0430\u0435\u0442? \u0421\u043a\u043e\u0440\u0435\u0435 \u0432\u0441\u0435\u0433\u043e, \u0432 \u044d\u0442\u043e\u0439 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438 \u0432\u0430\u043c \u043f\u043e\u043c\u043e\u0433\u0443\u0442 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":34931,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[27,1305],"class_list":["post-34930","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-matematika","tag-trigonometricheskie-podstanovki"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 - 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