{"id":732,"date":"2013-12-31T00:01:16","date_gmt":"2013-12-30T16:01:16","guid":{"rendered":"http:\/\/soniuch.net\/?page_id=732"},"modified":"2013-12-31T00:01:16","modified_gmt":"2013-12-30T16:01:16","slug":"%d1%82%d1%80%d0%b8%d0%b3%d0%be%d0%bd%d0%be%d0%bc%d0%b5%d1%82%d1%80","status":"publish","type":"page","link":"https:\/\/soniuch.net\/?page_id=732","title":{"rendered":"\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440"},"content":{"rendered":"

\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u044b\u043d \u0448\u0438\u043d\u0436 \u0447\u0430\u043d\u0430\u0440\u0443\u0443\u0434:<\/strong><\/span><\/p>\n

$$\\sin (-x) = – \\sin x$$<\/p>\n

$$\\cos (-x) = \\cos x$$<\/p>\n

$$\\textrm {tg} (-x) = – \\textrm{tg} x$$<\/p>\n

$$\\textrm{ctg} (-x) = – \\textrm{ctg} x$$<\/p>\n

$n$ \u043d\u044c \u0431\u04af\u0445\u044d\u043b \u0442\u043e\u043e \u0431\u043e\u043b \u0434\u0430\u0440\u0430\u0430\u0445 \u0442\u044d\u043d\u0446\u044d\u0442\u0433\u044d\u043b\u04af\u04af\u0434 \u0445\u04af\u0447\u0438\u043d\u0442\u044d\u0439:<\/p>\n

$$\\sin(x + 2\\pi n) = \\sin x$$<\/p>\n

$$\\cos(x + 2\\pi n) = \\cos x$$<\/p>\n

\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u0443\u0443\u0434\u044b\u043d \u0445\u043e\u043b\u0431\u043e\u043e:<\/strong><\/span><\/p>\n

$$\\sin^2 \\alpha + \\cos^2 \\alpha = 1$$<\/p>\n

$$\\textrm {tg} \\alpha = \\frac{\\sin \\alpha}{\\cos \\alpha}$$<\/p>\n

$$\\textrm{ctg} \\alpha = \\frac{\\cos \\alpha}{\\sin \\alpha}$$<\/p>\n

\u0414\u0430\u0432\u0445\u0430\u0440 \u04e9\u043d\u0446\u0433\u0438\u0439\u043d \u0445\u0430\u043c\u0430\u0430\u0440\u0430\u043b:<\/strong><\/span><\/p>\n

$$\\sin 2\\alpha = 2 \\sin \\alpha \\cos \\alpha = \\frac{2 \\textrm{tg} \\alpha}{1 + \\textrm{tg}^2 \\alpha }$$<\/p>\n

$$\\cos 2 \\alpha = \\cos^2 \\alpha – \\sin^2 \\alpha = 1 – 2 \\sin^2 \\alpha = \\frac{1 – \\textrm{tg}^2 \\alpha}{1 + \\textrm{tg}^2 \\alpha}$$<\/p>\n

$$\\textrm{tg} 2 \\alpha = \\frac{2 \\textrm{tg} \\alpha}{1 – \\textrm{tg}^2 \\alpha}$$<\/p>\n

\u0413\u0443\u0440\u0432\u0430\u043b\u0441\u0430\u043d \u04e9\u043d\u0446\u0433\u0438\u0439\u043d \u0445\u0430\u043c\u0430\u0430\u0440\u0430\u043b:<\/strong><\/span><\/p>\n

$$\\sin 3 \\alpha = 3 \\sin \\alpha – 4 \\sin^3 \\alpha$$<\/p>\n

$$\\cos 3 \\alpha = 4 \\cos^3 \\alpha – 3 \\cos \\alpha$$<\/p>\n

\u04e8\u043d\u0446\u0433\u0438\u0439\u043d \u043d\u0438\u0439\u043b\u0431\u044d\u0440 \u044f\u043b\u0433\u0430\u0432\u0430\u0440\u044b\u043d \u0445\u0443\u0432\u044c\u0434 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u04af\u04af\u0434:<\/strong><\/span><\/p>\n

$$\\sin(\\alpha \\pm \\beta) = \\sin \\alpha \\cos \\beta \\pm \\cos \\alpha \\sin \\beta$$<\/p>\n

$$\\cos(\\alpha \\pm \\beta) = \\cos \\alpha \\cos \\beta \\mp \\sin \\alpha \\sin \\beta$$<\/p>\n

$$\\textrm{tg}(\\alpha \\pm \\beta) = \\frac{\\textrm{tg} \\alpha \\pm \\textrm{tg} \\beta}{1 \\mp \\textrm{tg} \\alpha \\textrm{tg} \\beta}$$<\/p>\n

\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u04af\u04af\u0434\u0438\u0439\u043d \u043d\u0438\u0439\u043b\u0431\u044d\u0440 \u044f\u043b\u0433\u0430\u0432\u0430\u0440:<\/strong><\/span><\/p>\n

$$\\sin \\alpha + \\sin \\beta = 2 \\sin \\frac{\\alpha + \\beta}{2} \\cos \\frac {\\alpha – \\beta}{2}$$<\/p>\n

$$\\sin \\alpha – \\sin \\beta = 2 \\sin \\frac{\\alpha – \\beta}{2} \\cos \\frac {\\alpha + \\beta}{2}$$<\/p>\n

$$\\cos \\alpha + \\cos \\beta = 2 \\cos \\frac{\\alpha + \\beta}{2} \\cos \\frac {\\alpha – \\beta}{2}$$<\/p>\n

$$\\cos \\alpha – \\cos \\beta = – 2 \\sin \\frac{\\alpha + \\beta}{2} \\cos \\frac {\\alpha – \\beta}{2}$$<\/p>\n

$$\\textrm{tg} \\alpha \\mp \\textrm{tg} \\beta = \\frac{\\sin(\\alpha \\pm \\beta)}{\\cos \\alpha \\cos \\beta}$$<\/p>\n

\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u04af\u04af\u0434\u0438\u0439\u043d \u04af\u0440\u0436\u0432\u044d\u0440\u0438\u0439\u0433 \u043d\u0438\u0439\u043b\u0431\u044d\u0440 \u0431\u0443\u044e\u0443 \u044f\u043b\u0433\u0430\u0432\u0430\u0440\u0442 \u0437\u0430\u0434\u043b\u0430\u0445:<\/strong><\/span><\/p>\n

$$\\sin \\alpha \\sin \\beta = \\frac{1}{2} \\big( \\cos(\\alpha – \\beta) – \\cos(\\alpha + \\beta) \\big)$$<\/p>\n

$$\\cos \\alpha \\cos \\beta = \\frac{1}{2} \\big( \\cos(\\alpha – \\beta) + \\cos(\\alpha + \\beta) \\big)$$<\/p>\n

$$\\sin \\alpha \\cos \\beta = \\frac{1}{2} \\big( \\sin(\\alpha – \\beta) + \\sin(\\alpha + \\beta) \\big)$$<\/p>\n

\u0421\u0438\u043d\u0443\u0441\u044b\u043d \u0442\u0435\u043e\u0440\u0435\u043c:<\/strong><\/span><\/p>\n

\u0413\u0443\u0440\u0432\u0430\u043b\u0436\u043d\u044b \u0433\u0443\u0440\u0432\u0430\u043d \u0442\u0430\u043b\u0443\u0443\u0434 \u043d\u044c $a, b, c$ \u0431\u0430 \u0442\u044d\u0434\u0433\u044d\u044d\u0440\u0442 \u0445\u0430\u0440\u0433\u0430\u043b\u0437\u0430\u0445 \u04e9\u043d\u0446\u0433\u04af\u04af\u0434 \u043d\u044c $\\alpha, \\beta, \\gamma$ \u0431\u0430\u0439\u0432. \u0422\u044d\u0433\u0432\u044d\u043b \u044f\u043c\u0430\u0440 \u0447 \u0433\u0443\u0440\u0432\u0430\u043b\u0436\u043d\u044b \u0445\u0443\u0432\u044c\u0434 \u0434\u0430\u0440\u0430\u0430\u0445 \u0445\u0430\u0440\u044c\u0446\u0430\u0430 \u0445\u04af\u0447\u0438\u043d\u0442\u044d\u0439:<\/p>\n

$$\\frac{\\sin \\alpha}{a} = \\frac{\\sin \\beta}{b} = \\frac{\\sin \\gamma }{c}$$<\/p>\n

\u041a\u043e\u0441\u0438\u043d\u0443\u0441\u044b\u043d \u0442\u0435\u043e\u0440\u0435\u043c:<\/strong><\/span><\/p>\n

\u0413\u0443\u0440\u0432\u0430\u043b\u0436\u043d\u044b \u0433\u0443\u0440\u0432\u0430\u043d \u0442\u0430\u043b\u0443\u0443\u0434 \u043d\u044c $a, b, c$ \u0431\u0430 $a$ \u0442\u0430\u043b\u044b\u043d \u044d\u0441\u0440\u044d\u0433 \u0442\u0430\u043b\u0434 \u0431\u0430\u0439\u0445 \u04e9\u043d\u0446\u04e9\u0433 \u043d\u044c \u043d\u044c $\\alpha$ \u0431\u0430\u0439\u0432. \u0422\u044d\u0433\u0432\u044d\u043b \u044f\u043c\u0430\u0440 \u0447 \u0433\u0443\u0440\u0432\u0430\u043b\u0436\u043d\u044b \u0445\u0443\u0432\u044c\u0434 \u0434\u0430\u0440\u0430\u0430\u0445 \u0442\u044d\u043d\u0446\u044d\u0442\u0433\u044d\u043b \u0445\u04af\u0447\u0438\u043d\u0442\u044d\u0439:<\/p>\n

$$a^2 = b^2 + c^2 – 2bc \\cos \\alpha$$<\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u044b\u043d \u0448\u0438\u043d\u0436 \u0447\u0430\u043d\u0430\u0440\u0443\u0443\u0434: $$\\sin (-x) = – \\sin x$$ $$\\cos (-x) = \\cos x$$ $$\\textrm {tg} (-x) = – \\textrm{tg} x$$ $$\\textrm{ctg} (-x) = – \\textrm{ctg} x$$ $n$ \u043d\u044c \u0431\u04af\u0445\u044d\u043b \u0442\u043e\u043e \u0431\u043e\u043b \u0434\u0430\u0440\u0430\u0430\u0445 \u0442\u044d\u043d\u0446\u044d\u0442\u0433\u044d\u043b\u04af\u04af\u0434 \u0445\u04af\u0447\u0438\u043d\u0442\u044d\u0439: $$\\sin(x + 2\\pi n) = \\sin x$$ $$\\cos(x + 2\\pi n) = \\cos x$$ \u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0439\u043d \u0444\u0443\u043d\u043a\u0446\u0443\u0443\u0434\u044b\u043d \u0445\u043e\u043b\u0431\u043e\u043e: $$\\sin^2 \\alpha… Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":713,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-732","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages\/732","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/soniuch.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=732"}],"version-history":[{"count":0,"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages\/732\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/soniuch.net\/index.php?rest_route=\/wp\/v2\/pages\/713"}],"wp:attachment":[{"href":"https:\/\/soniuch.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=732"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}