{"id":10359,"date":"2023-07-07T21:11:32","date_gmt":"2023-07-07T13:11:32","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=10359"},"modified":"2025-03-24T12:39:18","modified_gmt":"2025-03-24T04:39:18","slug":"%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b0%e7%9b%b8%e5%85%b3%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=10359","title":{"rendered":"\u4e09\u89d2\u51fd\u6570\u516c\u5f0f"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a 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href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%92%8C\" >\u548c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E8%AF%B1%E5%AF%BC%E5%85%AC%E5%BC%8F\" >\u8bf1\u5bfc\u516c\u5f0f<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%85%AC%E5%BC%8F%E4%B8%80\" >\u516c\u5f0f\u4e00<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%85%AC%E5%BC%8F%E4%BA%8C\" >\u516c\u5f0f\u4e8c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%85%AC%E5%BC%8F%E4%B8%89\" >\u516c\u5f0f\u4e09<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%85%AC%E5%BC%8F%E5%9B%9B\" >\u516c\u5f0f\u56db<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%85%AC%E5%BC%8F%E4%BA%94\" >\u516c\u5f0f\u4e94<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%85%AC%E5%BC%8F%E5%85%AD\" >\u516c\u5f0f\u516d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E8%A7%84%E5%BE%8B\" >\u89c4\u5f8b<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%92%8C%E5%B7%AE%E5%85%AC%E5%BC%8F\" >\u548c\u5dee\u516c\u5f0f<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E4%BA%8C%E8%A7%92%E5%92%8C%E5%B7%AE\" >\u4e8c\u89d2\u548c\u5dee<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%92%8C%E5%B7%AE%E5%8C%96%E7%A7%AF\" >\u548c\u5dee\u5316\u79ef<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E7%A7%AF%E5%8C%96%E5%92%8C%E5%B7%AE\" >\u79ef\u5316\u548c\u5dee<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%80%8D%E8%A7%92%E5%85%AC%E5%BC%8F\" >\u500d\u89d2\u516c\u5f0f<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E4%BA%8C%E5%80%8D%E8%A7%92%E5%85%AC%E5%BC%8F\" >\u4e8c\u500d\u89d2\u516c\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E4%B8%89%E5%80%8D%E8%A7%92%E5%85%AC%E5%BC%8F\" >\u4e09\u500d\u89d2\u516c\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E5%8D%8A%E8%A7%92%E5%85%AC%E5%BC%8F\" >\u534a\u89d2\u516c\u5f0f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E8%BE%85%E5%8A%A9%E8%A7%92%E5%85%AC%E5%BC%8F\" >\u8f85\u52a9\u89d2\u516c\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E6%AD%A3%E5%BC%A6%E5%AE%9A%E7%90%86\" >\u6b63\u5f26\u5b9a\u7406<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/blog.iyatt.com\/?p=10359\/#%E4%BD%99%E5%BC%A6%E5%AE%9A%E7%90%86\" >\u4f59\u5f26\u5b9a\u7406<\/a><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E4%B9%89%E5%BC%8F\"><\/span>\u5b9a\u4e49\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p><img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2023\/07\/image-1688735261831.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 207px; --smush-placeholder-aspect-ratio: 207\/160;\" \/><\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l l l l}\n\u6b63\u5f26 &amp; \\sin A=\\frac{a}{c} &amp; \u4f59\u5272 &amp; \\csc A=\\frac{c}{a} \\\\\n\u4f59\u5f26 &amp; \\cos A=\\frac{b}{c} &amp; \u6b63\u5272 &amp; \\sec A=\\frac{c}{b} \\\\\n\u6b63\u5207 &amp; \\tan A=\\frac{a}{b} &amp; \u4f59\u5207 &amp; \\cot A=\\frac{b}{a}\n\\end{array}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E5%87%BD%E6%95%B0%E5%85%B3%E7%B3%BB\"><\/span>\u51fd\u6570\u5173\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E5%80%92%E6%95%B0\"><\/span>\u5012\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\tan\\alpha \\cot\\alpha=1 \\\\\n\\sin\\alpha \\csc\\alpha=1 \\\\\n\\cos\\alpha \\sec\\alpha=1\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%95%86%E6%95%B0\"><\/span>\u5546\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\tan\\alpha=\\frac{\\sin\\alpha}{\\cos\\alpha} \\\\\n\\cot\\alpha=\\frac{\\cos\\alpha}{\\sin\\alpha}\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%B9%B3%E6%96%B9\"><\/span>\u5e73\u65b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin^2\\alpha+\\cos^2\\alpha=1 \\\\\n1+\\tan^2\\alpha=\\sec^2\\alpha \\\\\n1+\\cot^2\\alpha=\\csc^2\\alpha\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%92%8C\"><\/span>\u548c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\arcsin x+\\arccos x=\\frac{\\pi}{2} \\\\\n\\arctan x+arccot\\ =\\frac{\\pi}{2}\n\\end{array}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E8%AF%B1%E5%AF%BC%E5%85%AC%E5%BC%8F\"><\/span>\u8bf1\u5bfc\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%8F%E4%B8%80\"><\/span>\u516c\u5f0f\u4e00<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code class=\"katex-inline\">k\\in Z<\/code><\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin(2k\\pi+\\alpha)=\\sin\\alpha \\\\\n\\cos(2k\\pi+\\alpha)=\\cos\\alpha \\\\\n\\tan(2k\\pi+\\alpha)=\\tan\\alpha \\\\\n\\cot(2k\\pi+\\alpha)=\\cot\\alpha\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%8F%E4%BA%8C\"><\/span>\u516c\u5f0f\u4e8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin(\\pi+\\alpha)=-\\sin\\alpha \\\\\n\\cos(\\pi+\\alpha)=-\\cos\\alpha \\\\\n\\tan(\\pi+\\alpha)=\\tan\\alpha \\\\\n\\cot(\\pi+\\alpha)=\\cot\\alpha\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%8F%E4%B8%89\"><\/span>\u516c\u5f0f\u4e09<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin(-\\alpha)=-\\sin\\alpha \\\\\n\\cos(-\\alpha)=\\cos\\alpha \\\\\n\\tan(-\\alpha)=-\\tan\\alpha \\\\\n\\cot(-\\alpha)=-\\cot\\alpha\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%8F%E5%9B%9B\"><\/span>\u516c\u5f0f\u56db<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin(\\pi-\\alpha)=\\sin\\alpha \\\\\n\\cos(\\pi-\\alpha)=-\\cos\\alpha \\\\\n\\tan(\\pi-\\alpha)=-\\tan\\alpha \\\\\n\\cot(\\pi-\\alpha)=-\\cot\\alpha\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%8F%E4%BA%94\"><\/span>\u516c\u5f0f\u4e94<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin(2\\pi-\\alpha)=-\\sin\\alpha \\\\\n\\cos(2\\pi-\\alpha)=\\cos\\alpha \\\\\n\\tan(2\\pi-\\alpha)=-\\tan\\alpha \\\\\n\\cot(2\\pi-\\alpha)=-\\cot\\alpha\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%8F%E5%85%AD\"><\/span>\u516c\u5f0f\u516d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin(\\frac{\\pi}{2}+\\alpha)=\\cos\\alpha \\\\\n\\cos(\\frac{\\pi}{2}+\\alpha)=-\\sin\\alpha \\\\\n\\tan(\\frac{\\pi}{2}+\\alpha)=-\\cot\\alpha \\\\\n\\cot(\\frac{\\pi}{2}+\\alpha)=-\\tan\\alpha \\\\\n\\ \\\\\n\\sin(\\frac{\\pi}{2}-\\alpha)=\\cos\\alpha \\\\\n\\cos(\\frac{\\pi}{2}-\\alpha)=\\sin\\alpha \\\\\n\\tan(\\frac{\\pi}{2}-\\alpha)=\\cot\\alpha \\\\\n\\cot(\\frac{\\pi}{2}-\\alpha)=\\tan\\alpha \\\\\n\\ \\\\\n\\sin(\\frac{3\\pi}{2}+\\alpha)=-\\cos\\alpha \\\\\n\\cos(\\frac{3\\pi}{2}+\\alpha)=\\sin\\alpha \\\\\n\\tan(\\frac{3\\pi}{2}+\\alpha)=-\\cot\\alpha \\\\\n\\cot(\\frac{3\\pi}{2}+\\alpha)=-\\tan\\alpha \\\\\n\\ \\\\\n\n\\sin(\\frac{3\\pi}{2}-\\alpha)=-\\cos\\alpha \\\\\n\\cos(\\frac{3\\pi}{2}-\\alpha)=-\\sin\\alpha \\\\\n\\tan(\\frac{3\\pi}{2}-\\alpha)=\\cot\\alpha \\\\\n\\cot(\\frac{3\\pi}{2}-\\alpha)=\\tan\\alpha\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E8%A7%84%E5%BE%8B\"><\/span>\u89c4\u5f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5947\u53d8\u5076\u4e0d\u53d8\uff0c\u7b26\u53f7\u770b\u8c61\u9650<br \/>\n<code class=\"katex-inline\">\\frac{\\pi}{2}k+\\alpha\uff0ck\\in Z<\/code><\/p>\n<pre><code class=\"language-katex\">\u5404\u8c61\u9650\u7b26\u53f7 \\\\\n\\ \\\\\nsin \\\\\n\\begin{array}{c | c}\n+ &amp; + \\\\\n\\hline\n- &amp; -\n\\end{array}\n\\ \\\\\ncos \\\\\n\\begin{array}{c | c}\n- &amp; + \\\\\n\\hline\n- &amp; +\n\\end{array}\n\\ \\\\\ntan \\\\\n\\begin{array}{c | c}\n- &amp; + \\\\\n\\hline\n+ &amp; -\n\\end{array}\n\\ \\\\\ncot \\\\\n\\begin{array}{c | c}\n- &amp; + \\\\\n\\hline\n+ &amp; -\n\\end{array}<\/code><\/pre>\n<p>\u89e3\u91ca<br \/>\nk \u4e3a\u5947\u6570\uff0c\u5219 sin \u53d8 cos\uff0ccos \u53d8 sin\uff0ctan \u53d8 cot\uff0ccot \u53d8 tan\uff0ck \u4e3a\u5076\u6570\u4e0d\u53d8<br \/>\n\u5c06<code class=\"katex-inline\">\\alpha<\/code> \u5f53\u4f5c\u9510\u89d2\uff0c<code class=\"katex-inline\">\\frac{\\pi}{2}k+\\alpha<\/code>\u5728\u54ea\u4e2a\u8c61\u9650\uff0c\u5bf9\u5e94\u4e09\u89d2\u51fd\u6570\u6b63\u8d1f<\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E5%92%8C%E5%B7%AE%E5%85%AC%E5%BC%8F\"><\/span>\u548c\u5dee\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E4%BA%8C%E8%A7%92%E5%92%8C%E5%B7%AE\"><\/span>\u4e8c\u89d2\u548c\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin(\\alpha+\\beta)=\\sin\\alpha \\cos\\beta+\\cos\\alpha \\sin\\beta \\\\\n\\sin(\\alpha-\\beta)=\\sin\\alpha \\cos\\beta - \\cos\\alpha \\sin\\beta \\\\\n\\cos(\\alpha+\\beta)=\\cos\\alpha \\cos\\beta - \\sin\\alpha \\sin\\beta \\\\\n\\cos(\\alpha-\\beta)=\\cos\\alpha \\cos\\beta + \\sin\\alpha \\sin\\beta \\\\\n\\ \\\\\n\\tan(\\alpha+\\beta)=\\frac{\\tan\\alpha+\\tan\\beta}{1-\\tan\\alpha \\tan\\beta} \\\\\ntan(\\alpha-\\beta)=\\frac{\\tan\\alpha-\\tan\\beta}{1+\\tan\\alpha \\tan\\beta} \\\\\ncot(\\alpha+\\beta)=\\frac{1-\\tan\\alpha \\tan\\beta}{\\tan\\alpha+\\tan\\beta} \\\\\ncot(\\alpha-\\beta)=\\frac{1+\\tan\\alpha \\tan\\beta}{\\tan\\alpha-\\tan\\beta}\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%92%8C%E5%B7%AE%E5%8C%96%E7%A7%AF\"><\/span>\u548c\u5dee\u5316\u79ef<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin\\alpha+\\sin\\beta=2\\sin\\frac{\\alpha+\\beta}{2}\\cos\\frac{\\alpha-\\beta}{2} \\\\\n\\sin\\alpha-\\sin\\beta=2\\cos\\frac{\\alpha+\\beta}{2}\\sin\\frac{\\alpha-\\beta}{2} \\\\\n\\cos\\alpha+\\cos\\beta=2\\cos\\frac{\\alpha+\\beta}{2}\\cos\\frac{\\alpha-\\beta}{2} \\\\\n\\cos\\alpha-\\cos\\beta=-2\\sin\\frac{\\alpha+\\beta}{2}\\sin\\frac{\\alpha-\\beta}{2} \\\\\n\\tan\\alpha+\\tan\\beta=\\frac{\\sin(\\alpha+\\beta)}{\\cos\\alpha\\cos\\beta}\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E7%A7%AF%E5%8C%96%E5%92%8C%E5%B7%AE\"><\/span>\u79ef\u5316\u548c\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\u2460\\sin\\alpha\\cos\\beta=\\frac{1}{2}[\\sin(\\alpha+\\beta)+\\sin(\\alpha-\\beta)] \\\\\n\u2461\\cos\\alpha\\sin\\beta=\\frac{1}{2}[\\sin(\\alpha+\\beta)-\\sin(\\alpha-\\beta)] \\\\\n\u2462\\sin\\alpha\\sin\\beta=-\\frac{1}{2}[\\cos(\\alpha+\\beta)-\\cos(\\alpha-\\beta)] \\\\\n\u2463\\cos\\alpha\\cos\\beta=\\frac{1}{2}[\\cos(\\alpha+\\beta)+\\cos(\\alpha-\\beta)] \\\\\n\\end{array}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E5%80%8D%E8%A7%92%E5%85%AC%E5%BC%8F\"><\/span>\u500d\u89d2\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E4%BA%8C%E5%80%8D%E8%A7%92%E5%85%AC%E5%BC%8F\"><\/span>\u4e8c\u500d\u89d2\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin2\\alpha=2\\sin\\alpha\\cos\\alpha \\\\\n\\cos2\\alpha=\\cos^2\\alpha-\\sin^2\\alpha=2\\cos^2\\alpha-1=1-2\\sin^2\\alpha \\\\\n\\tan2\\alpha=\\frac{2\\tan\\alpha}{1-\\tan^2\\alpha} \\\\\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E4%B8%89%E5%80%8D%E8%A7%92%E5%85%AC%E5%BC%8F\"><\/span>\u4e09\u500d\u89d2\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin3\\alpha=3\\sin\\alpha-4\\sin^3\\alpha=4\\sin\\alpha\\sin(\\frac{\\pi}{3}-\\alpha)\\sin(\\frac{\\pi}{3}+\\alpha) \\\\\n\\cos3\\alpha=4\\cos^3\\alpha-3\\cos\\alpha=4\\cos\\alpha\\cos(\\frac{\\pi}{3}-\\alpha)\\cos(\\frac{\\pi}{3}+\\alpha) \\\\\n\\tan3\\alpha=\\tan\\alpha\\tan(\\frac{\\pi}{3}-\\alpha)\\cos(\\frac{\\pi}{3}+\\alpha)\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%8D%8A%E8%A7%92%E5%85%AC%E5%BC%8F\"><\/span>\u534a\u89d2\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\sin\\frac{\\alpha}{2}=\\pm\\sqrt{\\frac{1-\\cos\\alpha}{2}} \uff0c\uff08\\sin^2\\alpha=\\frac{1-\\cos2\\alpha}{2}\uff09\\\\\n\\cos\\frac{\\alpha}{2}=\\pm\\sqrt{\\frac{1+\\cos\\alpha}{2}}\uff0c \uff08\\cos^2\\alpha=\\frac{1+\\cos2\\alpha}{2}\uff09\\\\\n\\tan\\frac{\\alpha}{2}=\\frac{\\sin\\alpha}{1+\\cos\\alpha}=\\frac{1-\\cos\\alpha}{\\sin\\alpha}=\\pm\\sqrt{\\frac{1-\\cos\\alpha}{1+\\cos\\alpha}} \\\\\n\\cot\\frac{\\alpha}{2}=\\frac{1+\\cos\\alpha}{\\sin\\alpha}=\\frac{\\sin\\alpha}{1-\\cos\\alpha}=\\pm\\sqrt{\\frac{1+\\cos\\alpha}{1-\\cos\\alpha}}\n\\end{array}<\/code><\/pre>\n<p>\u7b26\u53f7\u7531 <code class=\"katex-inline\">\\frac{\\alpha}{2}<\/code> \u6240\u5728\u8c61\u9650\u51b3\u5b9a<\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E8%BE%85%E5%8A%A9%E8%A7%92%E5%85%AC%E5%BC%8F\"><\/span>\u8f85\u52a9\u89d2\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<pre><code class=\"language-katex\">\\begin{array}{l}\na\\sin\\alpha+b\\cos\\alpha=\\sqrt{a^2+b^2}sin(\\alpha+\\phi)\uff0c \\\\\n\\phi=\\arctan\\frac{b}{a}\n\\end{array}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E6%AD%A3%E5%BC%A6%E5%AE%9A%E7%90%86\"><\/span>\u6b63\u5f26\u5b9a\u7406<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u5728\u4efb\u610f\u25b3ABC\u4e2d\uff0c\u89d2A\u3001B\u3001C\u6240\u5bf9\u7684\u8fb9\u957f\u5206\u522b\u4e3aa\u3001b\u3001c\uff0c\u4e09\u89d2\u5f62\u7684\u5916\u63a5\u5706\u534a\u5f84\u4e3aR\uff0c\u5219\u6709<br \/>\n<code class=\"katex-inline\">\\frac{a}{\\sin A}=\\frac{b}{\\sin b}=\\frac{c}{\\sin C}=2R<\/code><br \/>\n\u53ef\u5f97<\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l}\nS=\\frac{1}{2}ab\\sin C=\\frac{1}{2}ac\\sin B=\\frac{1}{2}bc\\sin A=\\frac{abc}{4R} \\\\\na=2R\\sin A\uff0cb=2R\\sin B\uff0cc=2R\\sin C \\\\\na:b:c=\\sin A:\\sin B:\\sin C\n\\end{array}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E4%BD%99%E5%BC%A6%E5%AE%9A%E7%90%86\"><\/span>\u4f59\u5f26\u5b9a\u7406<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<pre><code class=\"language-katex\">\\begin{array}{l}\na^2=b^2+c^2-2bc\\cos A \\\\\nb^2=a^2+c^2-2ac\\cos B \\\\\nc^2=a^2+b^2-2ab\\cos C \\\\\n\\ \\\\\n\\cos A=\\frac{b^2+c^2-a^2}{2bc} \\\\\n\\cos B=\\frac{a^2+c^2-b^2}{2ac} \\\\\n\\cos C=\\frac{a^2+b^2-c^2}{2ab}\n\\end{array}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u4e49\u5f0f \\begin{array}{l l l l} \u6b63\u5f26 &amp; \\sin A=\\frac{a}{c}  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[],"class_list":["post-10359","post","type-post","status-publish","format-standard","hentry","category-all","category-612"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10359","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10359"}],"version-history":[{"count":1,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10359\/revisions"}],"predecessor-version":[{"id":19672,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10359\/revisions\/19672"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10359"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10359"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10359"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}