
{"id":53636,"date":"2024-01-09T21:07:12","date_gmt":"2024-01-09T21:07:12","guid":{"rendered":"https:\/\/mathema.me\/?p=53636"},"modified":"2024-02-11T14:09:57","modified_gmt":"2024-02-11T14:09:57","slug":"osnovnye-trigonometricheskie-formuly","status":"publish","type":"post","link":"https:\/\/mathema.me\/ru\/blog\/osnovnye-trigonometricheskie-formuly\/","title":{"rendered":"\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \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.\u00a0\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u041e\u0441\u043d\u043e\u0432\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438, \u0432 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0430 \u043d\u0430\u0447\u0438\u043d\u0430\u044e\u0442 \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0432 8-\u043c \u043a\u043b\u0430\u0441\u0441\u0435, \u043f\u0440\u043e\u0434\u043e\u043b\u0436\u0430\u044e\u0442 \u0432 9-\u043c.&nbsp;\u042d\u0442\u043e\u0442 \u0440\u0430\u0437\u0434\u0435\u043b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u043b\u0435\u0436\u0438\u0442 \u043d\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0435 \u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0441\u0430\u043c\u044b\u0445 \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u0442\u0435\u043c \u0432 \u0448\u043a\u043e\u043b\u044c\u043d\u043e\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0435.&nbsp;\u041d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0430\u044f \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0437\u0430\u043f\u043e\u043c\u0438\u043d\u0430\u043d\u0438\u0438 \u0431\u043e\u043b\u044c\u0448\u043e\u0433\u043e \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0430 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u043e\u0440\u043c\u0443\u043b.&nbsp;Mathema \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u0438\u043b\u0430 \u0441\u0442\u0430\u0442\u044c\u044e \u0441 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u043c\u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438, \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0443\u0433\u043b\u043e\u0432, \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0430\u043c\u0438 \u0438 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043f\u043e\u043b\u0435\u0437\u043d\u044b\u043c\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0430\u043c\u0438.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0427\u0442\u043e \u043d\u0443\u0436\u043d\u043e \u0437\u043d\u0430\u0442\u044c \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u043e\u0440\u043c\u0443\u043b<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u2013 \u044d\u0442\u043e \u0440\u0430\u0437\u0434\u0435\u043b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438, \u0438\u0437\u0443\u0447\u0430\u044e\u0449\u0438\u0439 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0430\u043c\u0438 \u0438 \u0443\u0433\u043b\u0430\u043c\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432.&nbsp;\u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u043e\u0440\u043c\u0443\u043b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u043c\u043e\u0433\u0443\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u0443\u0433\u043b\u043e\u0432.<\/li>\n\n\n\n<li>\u0421\u0438\u043d\u0443\u0441 \u2014 \u0432 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u043c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0435 \u0441\u0438\u043d\u0443\u0441 \u043e\u0441\u0442\u0440\u043e\u0433\u043e \u0443\u0433\u043b\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u043a \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u043e\u0433\u043e \u043a\u0430\u0442\u0435\u0442\u0430 \u043a \u0433\u0438\u043f\u043e\u0442\u0435\u043d\u0443\u0437\u0435<\/li>\n\n\n\n<li>\u041a\u043e\u0441\u0438\u043d\u0443\u0441 \u2013 \u0432 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u043c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0435 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u043e\u0441\u0442\u0440\u043e\u0433\u043e \u0443\u0433\u043b\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u043a \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043f\u0440\u0438\u043b\u0435\u0433\u0430\u044e\u0449\u0435\u0433\u043e \u043a\u0430\u0442\u0435\u0442\u0430 \u043a \u0433\u0438\u043f\u043e\u0442\u0435\u043d\u0443\u0437\u0435.<\/li>\n\n\n\n<li>\u0422\u0430\u043d\u0433\u0435\u043d\u0441 \u2013 \u044d\u0442\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u0434\u043b\u0438\u043d\u044b \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u043e\u0433\u043e \u043a\u0430\u0442\u0435\u0442\u0430 \u043a \u0434\u043b\u0438\u043d\u0435 \u0431\u043b\u0438\u0437\u043b\u0435\u0436\u0430\u0449\u0435\u0433\u043e \u043a\u0430\u0442\u0435\u0442\u0430.<\/li>\n\n\n\n<li>\u041a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441 \u2013 \u044d\u0442\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u0434\u043b\u0438\u043d\u044b \u0431\u043b\u0438\u0437\u043b\u0435\u0436\u0430\u0449\u0435\u0433\u043e \u043a\u0430\u0442\u0435\u0442\u0430 \u043a \u0434\u043b\u0438\u043d\u0435 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u043e\u0433\u043e \u043a\u0430\u0442\u0435\u0442\u0430<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \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:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u042d\u0442\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u0438\u0433\u043e\u0434\u044f\u0442\u0441\u044f \u043f\u0440\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0432 \u0448\u043a\u043e\u043b\u044c\u043d\u043e\u0439 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0435.&nbsp;\u0417\u0434\u0435\u0441\u044c \u0441\u043e\u0431\u0440\u0430\u043d\u044b \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044b \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 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0443\u0433\u043b\u043e\u0432.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u0421\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0442\u043e\u0433\u043e \u0436\u0435 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\\[\\sin^2a+\\cos^2a\\;=\\;1,\\;\u0430\\in R\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[tg\\;a=\\frac{\\sin\\;a}{\\cos\\;a},\\;\u0430\\;\\neq\\frac\\pi2+\\pi n,\\;n\\;\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[tg\\;a\\;\\cdot ctg\\;a\\;=\\;1,\\;a\\neq\\frac{\\pi n}2,\\;n\\;\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[1+tg^2a=\\frac1{\\cos^{2\\;}a},\\;a\\neq\\frac\\pi2+\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[1+ctg^2a=\\frac1{\\sin^{2\\;}a},\\;a\\neq\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\\[\\sin(a\\pm b)=\\sin a\\cdot\\cos b\\pm\\cos a\\cdot\\sin b\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[\\cos(a\\pm b)=\\mathrm{cosa}\\cdot\\cos b\\pm\\sin a\\cdot\\mathrm{sinb}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[tg(a\\pm b)=\\frac{tg\\;a+tg\\;b}{1\\pm tg\\;a\\cdot tg\\;b},\\;a\\neq\\frac\\pi2+\\pi n,\\;b\\neq\\frac\\pi2+\\pi n,\\;a\\pm b\\neq\\frac\\pi2+\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[ctg\\;(a\\;\\pm b)\\;=\\;\\frac{ctg\\;a\\cdot ctg\\;b\\pm1}{ctg\\;a\\pm ctg\\;b},a\\neq\\pi n,\\;b\\neq\\pi n,\\;a\\pm b\\neq\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u0432\u043e\u0439\u043d\u043e\u0433\u043e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\\[\\sin2a=2\\sin a\\cdot\\cos a\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[\\cos2a=\\cos^2a-\\sin^2a\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[tg\\;2a\\;=\\;\\frac{2tg\\;a}{1-\\;tg^2a},\\;a\\neq\\frac\\pi4+\\pi n,\\;a\\neq\\frac\\pi2+\\pi n,\\;n\\;\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[ctg\\;2a\\;=\\;\\frac{ctg^2\\;a-1}{2tg\\;a},\\;a\\neq\\frac{\\pi\\kappa}2,\\;n\\;\\in\\mathbb{Z}\\]<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u0442\u0440\u043e\u0439\u043d\u043e\u0433\u043e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\\[\\sin3a=3\\sin a-4\\sin^3a\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[\\cos3a=4\\cos^3a-3\\cos a\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[tg3a=\\frac{3tg\\;a-tg^3a}{1-3tg^2a},\\;a\\neq\\frac\\pi6(2n+1),\\;n\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[ctg3a=\\frac{3ctg\\;a-ctg^3a}{1-3ctg^2a},\\;a\\neq\\frac{\\pi n}3,\\;n\\in\\mathbb{Z}\\]<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0441\u043d\u0438\u0436\u0435\u043d\u0438\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\\[\\sin^2a=\\frac{1-\\cos2a}2\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[\\cos^2a=\\frac{1+\\cos2a}2\\]<\/p>\n<\/blockquote>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \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 \u0432 \u0441\u0443\u043c\u043c\u0443<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\\[\\sin a\\cdot\\sin b=\\frac12(\\cos(a-b)-(\\cos(a+b))\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[\\cos a\\cdot\\cos b=\\frac12(\\cos(a-b)+(\\cos(a+b))\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[\\sin a\\cdot\\cos b=\\frac12(\\sin(a-b)+(\\sin(a+b))\\]<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u0424\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u043d\u043e\u0433\u043e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\\[sina2=\u00b11-cosa2\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[\\cos\\frac a2=\\pm\\sqrt{\\frac{1+\\cos a}2}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[tg\\frac a2=\\pm\\sqrt{\\frac{1-\\cos a}{1+\\cos\\;a}}=\\frac{\\sin a}{1+\\cos a},\\;a\\neq\\pi+2\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[tg\\frac a2=\\frac{1-\\cos a}{\\sin a},\\;a\\neq\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[ctg\\frac a2=\\pm\\sqrt{\\frac{1+\\cos a}{1-\\cos a}}=\\;\\frac{\\sin a}{1-\\cos a},\\;a\\neq2\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\[ctg\\frac a2=\\frac{1+\\cos a}{\\sin a}\\;,\\;a\\neq\\pi n,\\;n\\in\\mathbb{Z}\\]<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0443\u0433\u043b\u043e\u0432<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412 \u044d\u0442\u043e\u0439 \u0442\u0430\u0431\u043b\u0438\u0446\u0435 \u0437\u0430\u043f\u0438\u0441\u0430\u043d\u044b \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0441\u0438\u043d\u0443\u0441\u043e\u0432, \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u043e\u0432, \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u043e\u0432 \u0438 \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441\u043e\u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0443\u0433\u043b\u043e\u0432, \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0447\u0430\u0441\u0442\u043e \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0449\u0438\u0445\u0441\u044f \u0432 \u0448\u043a\u043e\u043b\u044c\u043d\u043e\u0439 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438.&nbsp;\u0422\u0430\u043a\u0443\u044e \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e \u0434\u0435\u0440\u0436\u0430\u0442\u044c \u043f\u043e\u0434 \u0440\u0443\u043a\u043e\u0439, \u0438\u043b\u0438 \u043f\u043e\u043f\u044b\u0442\u0430\u0442\u044c\u0441\u044f \u0437\u0430\u043f\u043e\u043c\u043d\u0438\u0442\u044c \u0435\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435.&nbsp;\u0421\u0434\u0435\u043b\u0430\u0442\u044c \u044d\u0442\u043e \u043f\u0440\u043e\u0449\u0435, \u0447\u0435\u043c \u043a\u0430\u0436\u0435\u0442\u0441\u044f, \u0432\u0435\u0434\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u044e\u0442\u0441\u044f.&nbsp;\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, tg 30\u00b0 \u0440\u0430\u0432\u043d\u043e ctg 60\u00b0 \u0438 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442 tg60\u00b0 \u0440\u0430\u0432\u043d\u043e ctg30\u00b0.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular has-medium-font-size\"><table class=\"has-background\" style=\"background:linear-gradient(180deg,rgb(255,255,255) undefined%,rgb(6,147,227) 40%,rgba(155,81,224,0) 42%)\"><tbody><tr><td><strong>t \u0433\u0440\u0430\u0434<\/strong><\/td><td><strong>0<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>30\u00b0<\/strong><br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>45\u00b0<\/strong><br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>60\u00b0<\/strong><br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>90\u00b0<\/strong><br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>180\u00b0<\/strong><br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>270\u00b0<\/strong><br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>360\u00b0<\/strong><br><\/td><\/tr><tr><td><strong>sin t<\/strong><\/td><td>0<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac12\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac{\\sqrt2}2\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac{\\sqrt3}2\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td><strong>cos t<\/strong><\/td><td>1<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac{\\sqrt3}2\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac{\\sqrt2}2\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac12\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td><strong>tg t<\/strong><\/td><td>0<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac{\\sqrt3}3\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\sqrt3\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">&#8211;<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">&#8211;<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td><strong>ctg t<\/strong><\/td><td>&#8211;<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\sqrt3\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">\\[\\frac{\\sqrt3}3\\]<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">&#8211;<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">&#8211;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u0427\u0442\u043e \u0438\u0437\u0443\u0447\u0430\u0435\u0442 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u2013 \u044d\u0442\u043e \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u0437\u0443\u0447\u0430\u0435\u0442 \u0432\u0437\u0430\u0438\u043c\u043e\u0441\u0432\u044f\u0437\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\u043e\u0432.&nbsp;\u0421\u0430\u043c\u043e \u0441\u043b\u043e\u0432\u043e &#8220;\u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f&#8221; \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0433\u0440\u0435\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u043b\u043e\u0432 &#8220;\u0442\u0440\u03af\u03b1&#8221; (\u0442\u0440\u0438) \u0438 &#8220;\u03b3\u03c9\u03bd\u03af\u03b1&#8221; (\u0443\u0433\u043e\u043b).&nbsp;\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 \u043d\u0430\u043c \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c, \u043a\u0430\u043a \u0438\u0437\u043c\u0435\u043d\u044f\u044e\u0442\u0441\u044f \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u0438\u0437\u043c\u0435\u043d\u044f\u0435\u043c \u0435\u0433\u043e \u0443\u0433\u043b\u044b.&nbsp;\u042d\u0442\u043e \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0440\u0435\u0448\u0430\u0442\u044c \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439, \u0432\u044b\u0441\u043e\u0442 \u0437\u0434\u0430\u043d\u0438\u0439, \u0443\u0433\u043b\u043e\u0432 \u043d\u0430 \u043a\u0430\u0440\u0442\u0435 \u0438 \u043c\u043d\u043e\u0433\u043e\u0435 \u0434\u0440\u0443\u0433\u043e\u0435.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0435\u0441\u043b\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0438 \u043c\u044b \u0437\u043d\u0430\u0435\u043c \u043e\u0434\u0438\u043d \u0443\u0433\u043e\u043b \u0438 \u0434\u043b\u0438\u043d\u0443 \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0435\u0433\u043e \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u044b, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c \u0434\u043b\u0438\u043d\u0443 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u044b \u044d\u0442\u043e\u0433\u043e \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0448\u0438\u0440\u043e\u043a\u0438\u0439 \u0441\u043f\u0435\u043a\u0442\u0440 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0432 \u0442\u0430\u043a\u0438\u0445 \u043d\u0430\u0443\u043a\u0430\u0445, \u043a\u0430\u043a \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u0438\u044f, \u0430\u0441\u0442\u0440\u043e\u043d\u043e\u043c\u0438\u044f, \u0444\u0438\u0437\u0438\u043a\u0430, \u043a\u043e\u043c\u043f\u044c\u044e\u0442\u0435\u0440\u043d\u0430\u044f \u0433\u0440\u0430\u0444\u0438\u043a\u0430, \u043c\u0435\u0434\u0438\u0446\u0438\u043d\u0430 \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u043d\u0430\u0443\u043a\u0438.&nbsp;\u0418\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u0440\u0430\u0437\u0432\u0438\u0442\u044c \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043c\u044b\u0448\u043b\u0435\u043d\u0438\u0435 \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043d\u0430\u0432\u044b\u043a\u0438 \u0438 \u043d\u0430\u0439\u0442\u0438 \u043e\u0442\u0432\u0435\u0442\u044b \u043d\u0430 \u0440\u0430\u0437\u043d\u044b\u0435 \u0432\u043e\u043f\u0440\u043e\u0441\u044b, \u043a\u0430\u0441\u0430\u044e\u0449\u0438\u0435\u0441\u044f \u0443\u0433\u043b\u043e\u0432 \u0438 \u0441\u0442\u0440\u0430\u043d\u0438\u0446 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041e\u0441\u043d\u043e\u0432\u044b \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0438, \u0432 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0430 \u043d\u0430\u0447\u0438\u043d\u0430\u044e\u0442 \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0432 8-\u043c \u043a\u043b\u0430\u0441\u0441\u0435, \u043f\u0440\u043e\u0434\u043e\u043b\u0436\u0430\u044e\u0442 \u0432 9-\u043c.&nbsp;\u042d\u0442\u043e\u0442 \u0440\u0430\u0437\u0434\u0435\u043b 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