{"id":2915,"date":"2024-10-08T11:25:48","date_gmt":"2024-10-08T03:25:48","guid":{"rendered":"http:\/\/jhwk.online\/?p=2915"},"modified":"2024-10-08T11:25:48","modified_gmt":"2024-10-08T03:25:48","slug":"hsyldwt-5-3-4-5","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=2915","title":{"rendered":"\u4e09\u89d2\u51fd\u6570\u7684\u6982\u5ff5\u53ca\u516c\u5f0f"},"content":{"rendered":"\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-711932c\" data-block-id=\"711932c\"><\/div>\n\n\n\n<div class=\"wp-block-ht-block-toc  is-style-outline htoc htoc--position-wide toc-list-style-plain\" data-htoc-state=\"expanded\"><span class=\"htoc__title\"><span class=\"ht_toc_title\">\u76ee\u5f55<\/span><span class=\"htoc__toggle\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\"><g fill=\"#444\"><path d=\"M15 7H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1z\"><\/path><path d=\"M15 1H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1zM15 13H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1z\"><\/path><\/g><\/svg><\/span><\/span><div class=\"htoc__itemswrap\"><ul class=\"ht_toc_list\"><li class=\"\"><a href=\"\/#htoc-111111111111111\">\u4efb\u610f\u89d2\u3001\u4e09\u89d2\u51fd\u6570\u7684\u6982\u5ff5<\/a><\/li><li class=\"\"><a href=\"\/#htoc-11111111\">\u4e09\u89d2\u516c\u5f0f\u7684\u5e94\u7528<\/a><\/li><li class=\"\"><a href=\"\/#htoc-1111111111111111\">\u7528\u5df2\u77e5\u89d2\u8868\u793a\u6240\u6c42\u89d2<\/a><\/li><\/ul><\/div><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-111111111111111\">\u4efb\u610f\u89d2\u3001\u4e09\u89d2\u51fd\u6570\u7684\u6982\u5ff5<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.(1)\u5df2\u77e5  \\alpha  \u662f\u7b2c\u4e8c\u8c61\u9650\u89d2, \u90a3\u4e48  \\frac{\\alpha}{2}  \u662f(~~)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.\u7b2c\u4e00\u8c61\u9650\u89d2~~\nB.\u7b2c\u4e8c\u8c61\u9650\u89d2~~\nC.\u7b2c\u4e00\u6216\u7b2c\u4e8c\u8c61\u9650\u89d2~~\nD.\u7b2c\u4e00\u6216\u7b2c\u4e09\u8c61\u9650\u89d2~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(2)\u5df2\u77e5  \\alpha  \u662f\u7b2c\u4e8c\u8c61\u9650\u89d2, \u90a3\u4e48  \\frac{\\alpha}{3}  \u662f(~~)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.\u7b2c\u4e8c\u6216\u7b2c\u4e09\u6216\u7b2c\u56db\u8c61\u9650\u89d2~~\nB.\u7b2c\u4e00\u6216\u7b2c\u4e8c\u6216\u7b2c\u4e09\u8c61\u9650\u89d2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nC.\u7b2c\u4e00\u6216\u7b2c\u4e8c\u6216\u7b2c\u56db\u8c61\u9650\u89d2~~\nD.\u7b2c\u4e00\u6216\u7b2c\u4e09\u6216\u7b2c\u56db\u8c61\u9650\u89d2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-d-2-c-alpha-in-left-frac-pi-2-2k-pi-pi-2k-pi-right-k-in-z-frac-alpha-2-in-left-frac-pi-4-k-pi-frac-pi-2-k-pi-right-k-in-z-frac-alpha-3-in-left-frac-pi-6-frac-2k-pi-3-frac-pi-3-frac-2k-pi-3-right-k-in-z\"><pre>\u7b54\u6848\uff1a(1)D,(2)C;\u63d0\u793a\uff1a\\alpha \\in \\left ( \\frac{\\pi }{2}+2k\\pi , \\pi +2k \\pi  \\right ) ,k\\in{Z},\u5219\\frac{\\alpha }{2} \\in \\left ( \\frac{\\pi }{4}+k\\pi , \\frac{\\pi }{2} +k \\pi  \\right ) ,~\\\\k\\in{Z}\uff0c\u5728\u4e00\u3001\u4e09\u8c61\u9650;\\frac{\\alpha }{3} \\in \\left ( \\frac{\\pi }{6}+\\frac{2k\\pi}{3} , \\frac{\\pi }{3} +\\frac{2k\\pi}{3} \\right ) ,k\\in{Z}\uff0c\u5728\u7b2c\u4e00\u6216\u7b2c\u4e8c\u6216\u7b2c\u56db\u8c61\u9650.<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u82e5\\sin x \\cos x&gt;0,\\sin x +\\cos x&gt;0,\u5219\\frac{x}{2}\u662f(~~)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\A.\u7b2c\u4e00\u8c61\u9650\u89d2~~\nB.\u7b2c\u4e8c\u8c61\u9650\u89d2~~\nC.\u7b2c\u4e00\u6216\u7b2c\u4e8c\u8c61\u9650\u89d2~~\nD.\u7b2c\u4e00\u6216\u7b2c\u4e09\u8c61\u9650\u89d2~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-d-x\"><pre>\u7b54\u6848\uff1aD;\u63d0\u793a\uff1ax\u4e3a\u7b2c\u4e00\u8c61\u9650\u89d2\uff0c\u539f\u7406\u540c\u4e0a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u5316\u7b80  \\sqrt{\\frac{1+\\sin \\alpha}{1-\\sin \\alpha}}-\\sqrt{\\frac{1-\\sin \\alpha}{1+\\sin \\alpha}} , \u5176\u4e2d  \\alpha  \u4e3a\u7b2c\u4e8c\u8c61\u9650\u89d2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-2-tan-alpha-rightarrow-sqrt-frac-1-sin-alpha-2-1-sin-2-alpha-sqrt-frac-1-sin-alpha-2-1-sin-2-alpha\"><pre>\u7b54\u6848:-2\\tan \\alpha;\u63d0\u793a\uff1a\u539f\u5f0f\\Rightarrow \\sqrt{\\frac{(1+\\sin \\alpha)^2}{1-\\sin^2 \\alpha}}-\\sqrt{\\frac{(1-\\sin \\alpha)^2}{1-\\sin^2 \\alpha}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u5df2\u77e5\u89d2  \\alpha  \u7684\u9876\u70b9\u4e3a\u5750\u6807\u539f\u70b9, \u59cb\u8fb9\u4e3a  x  \u8f74\u7684\u975e\u8d1f\u534a\u8f74, \u82e5\u70b9  P(\\sin \\alpha ,  \\boldsymbol{\\operatorname { t a n }} \\alpha  )\u5728\u7b2c\u56db\u8c61\u9650, ~~~\\\\\u5219\u89d2  \\alpha  \u7684\u7ec8\u8fb9\u5728(  ~~)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA. \u7b2c\u4e00\u8c61\u9650~~\nB. \u7b2c\u4e8c\u8c61\u9650~~\nC. \u7b2c\u4e09\u8c61\u9650~~\nD. \u7b2c\u56db\u8c61\u9650~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-b-p-sin-alpha-boldsymbol-operatorname-t-a-n-alpha-sin-alpha-gt-0-tan-alpha-lt-0-therefore-alpha\"><pre>\u7b54\u6848\uff1aB;\u63d0\u793a\uff1a P(\\sin \\alpha ,  \\boldsymbol{\\operatorname { t a n }} \\alpha  )\u5728\u7b2c\u56db\u8c61\u9650,\\sin \\alpha &gt;0\u4e14 \\tan {\\alpha}&lt;0,\\therefore \\alpha\u5728\u7b2c\u4e8c\u8c61\u9650.~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.\u5df2\u77e5\u89d2  \\alpha  \u7684\u7ec8\u8fb9\u4e0a\u6709\u4e00\u70b9  P  \u7684\u5750\u6807\u662f  (3 a, 4 a) , \u5176\u4e2d  a \\neq 0 ,\u6c42  \\sin \\alpha, \\cos \\alpha, \\tan \\alpha  \u7684\u503c.~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-a-gt-0-a-1-sin-alpha-frac-4-5-cos-alpha-frac-3-5-tan-alpha-frac-4-3-a-gt-0-a-1-sin-alpha-frac-4-5-cos-alpha-frac-3-5-tan-alpha-frac-4-3\"><pre>\u7b54\u6848\uff1aa&gt;0, \u53ef\u4ee4a=1,\\sin \\alpha=\\frac{4}{5}, \\cos \\alpha=\\frac{3}{5},  \\tan \\alpha=\\frac{4}{3};~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\a&lt;0, \u53ef\u4ee4a=-1,\\sin \\alpha=-\\frac{4}{5}, \\cos \\alpha=-\\frac{3}{5},  \\tan \\alpha=\\frac{4}{3} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.\n\u5df2\u77e5\u89d2  \\alpha  \u7684\u7ec8\u8fb9\u8fc7\u70b9  P\\left(-8 m,-6 \\sin 30^{\\circ}\\right) , \u4e14  \\cos \\alpha=-\\frac{4}{5} , \u5219  m  \u7684\u503c\u4e3a ( ~~)~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.  -\\frac{1}{2} ~~\nB.  -\\frac{\\sqrt{3}}{2} ~~\nC.  \\frac{1}{2} ~~\nD.  \\frac{\\sqrt{3}}{2} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-c-p-8-m-3-r-sqrt-64-m-2-9-cos-alpha-frac-8-m-sqrt-64-m-2-9-frac-4-5-m-gt-0-m-frac-1-2\"><pre>\u7b54\u6848: C;\n\u63d0\u793a\uff1a \u7531\u9898\u610f\u5f97\u70b9  P(-8 m,-3) ,\n\nr=\\sqrt{64 m^{2}+9}\n\n\n\u6240\u4ee5  \\cos \\alpha=\\frac{-8 m}{\\sqrt{64 m^{2}+9}}~~~~~~\\\\=-\\frac{4}{5} ,\n\u6240\u4ee5  m&gt;0 , \u89e3\u5f97  m=\\frac{1}{2} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>7.\u5df2\u77e5\u89d2  \\alpha  \u7684\u59cb\u8fb9\u4e0e  x  \u8f74\u975e\u8d1f\u534a\u8f74\u91cd\u5408, \u7ec8\u8fb9\u5728\u76f4\u7ebf  y=4 x  \u4e0a\uff0c\u6c42  \\frac{\\sin \\alpha-2 \\cos \\alpha}{\\tan \\alpha}  \u7684\u503c.~~~~\\\\\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-frac-sqrt-17-34-frac-sqrt-17-34-1-4-cos-alpha-frac-1-sqrt-17-sin-alpha-frac-4-sqrt-17-tan-alpha-4-1-4-cos-alpha-frac-1-sqrt-17-sin-alpha-frac-4-sqrt-17-tan-alpha-4-y-4x-tan-alpha-4-sin-alpha-cos-alpha\"><pre>\u7b54\u6848\uff1a\\frac{\\sqrt{17}}{34} \n\u6216 -\\frac{\\sqrt{17}}{34} ;\u63d0\u793a:\u5728\u7b2c\u4e00\u8c61\u9650\u53d6\u70b9(1,4),\u5f97  \\cos \\alpha=\\frac{1}{\\sqrt{17}}, \\sin \\alpha=\\frac{4}{\\sqrt{17}}, ~~~~~~~\\\\\\tan \\alpha=4 ;\u5728\u7b2c\u4e09\u8c61\u9650\u53d6\u70b9(-1,-4),\u5f97  \\cos \\alpha=-\\frac{1}{\\sqrt{17}}, \\sin \\alpha=-\\frac{4}{\\sqrt{17}}, \\tan \\alpha=4 .~~~~~~~~~\\\\\u2605\u6ce8\uff1a\u7531y=4x,\\tan \\alpha=4,\\sin \\alpha\u548c\\cos \\alpha\u4e0d\u552f\u4e00.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>8.(1)\u5df2\u77e5  \\sin \\alpha=-\\frac{3}{5} , \u6c42  \\cos \\alpha, \\tan \\alpha  \u7684\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n\n<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(2)\u5df2\u77e5  \\tan \\varphi=-\\sqrt{3} , \u6c42  \\sin \\varphi, \\cos \\varphi  \u7684\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(3)\u6c42\u503c\uff1a\\cos 225^{\\circ};\\sin \\frac{11 \\pi}{3};\\sin \\left(-\\frac{16 \\pi}{3}\\right);\\cos \\frac{65 \\pi}{6}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-alpha-cos-alpha-frac-4-5-tan-alpha-frac-3-4-alpha-cos-alpha-frac-4-5-tan-alpha-frac-3-4-2-alpha-sin-alpha-frac-sqrt-3-2-cos-alpha-frac-1-2-alpha-sin-alpha-frac-sqrt-3-2-cos-alpha-frac-1-2-y-sqrt-3-x-1-sin-x-cos-x\"><pre>\u7b54\u6848:(1)\\alpha\u4e3a\u7b2c\u4e09\u8c61\u9650\u89d2\u65f6\uff0c \\cos \\alpha=-\\frac{4}{5}, \\tan \\alpha  =\\frac{3}{4};\\alpha\u4e3a\u7b2c\u56db\u8c61\u9650\u89d2\u65f6\uff0c~~~~~~~~~~~~~~~~~~~~~\\\\ \\cos \\alpha=\\frac{4}{5}, \\tan \\alpha  =-\\frac{3}{4}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(2)\\alpha\u4e3a\u7b2c\u4e8c\u8c61\u9650\u89d2\u65f6\uff0c \\sin \\alpha=\\frac{\\sqrt{3}}{2}, \\cos \\alpha  =-\\frac{1}{2};\\alpha\u4e3a\u7b2c\u56db\u8c61\u9650\u89d2\u65f6\uff0c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\ \\sin \\alpha=-\\frac{\\sqrt{3}}{2}, \\cos \\alpha  =\\frac{1}{2}.\u2605\u6ce8\uff1a\u53ef\u4ee4y=\\sqrt{3},x=1,\u5feb\u901f\u6c42|\\sin x|\u548c|\\cos x|,\u518d\u52a0\u7b26\u53f7.\\\\(3)-\\frac{\\sqrt{2} }{2} ;-\\frac{\\sqrt{3} }{2};\\frac{\\sqrt{3} }{2};-\\frac{\\sqrt{3} }{2}.\u63d0\u793a:\u6839\u636e\u5bf9\u79f0\u6027\u8f6c\u5316\u5230\u7b2c\u4e00\u8c61\u9650\u89d2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre><\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-1dda9ec\" data-block-id=\"1dda9ec\"><style>.stk-1dda9ec {height:30px !important;}<\/style><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-11111111\">\u4e09\u89d2\u516c\u5f0f\u7684\u5e94\u7528<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\n\n\u5df2\u77e5  \\tan \\alpha=2 , (1)\u6c42  \\frac{\\sin \\alpha+\\cos \\alpha}{\\sin \\alpha-\\cos \\alpha}  \u7684\u503c;(2)\u6c42\\sin \\alpha\\cos \\alpha;(3)\\cos ^2{\\alpha+\\sin 2\\alpha.}~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-3-2-frac-2-5-3-1-tan-alpha\"><pre>\u7b54\u6848:(1)3;(2)\\frac{2}{5};(3)1;\u63d0\u793a\uff1a\u5229\u7528\u9f50\u6b21\u5f0f\uff0c\u8f6c\u5316\u4e3a\\tan \\alpha.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u82e5  \\frac{1-\\tan \\left(\\alpha-\\displaystyle \\frac{\\pi}{4}\\right)}{1+\\tan \\left(\\alpha-\\displaystyle\\frac{\\pi}{4}\\right)}=\\displaystyle\\frac{1}{2} ,\u6c42  \\cos 2 \\alpha  \u7684\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-a-rightarrow-tan-left-alpha-frac-pi-4-right-frac-1-3-rightarrow-tan-alpha-2-therefore-cos-2-alpha-cos-2-alpha-sin-2-alpha-frac-1-tan-2-alpha-1-tan-2-alpha-frac-3-5\"><pre>\u7b54\u6848: -\\frac{3}{5} ; \u63d0\u793a\uff1a \u7531\u5df2\u77e5  \\Rightarrow \\tan \\left(\\alpha-\\frac{\\pi}{4}\\right)=\\frac{1}{3}, \\Rightarrow \\tan \\alpha=2, \\therefore \\cos 2 \\alpha=\\cos ^{2} \\alpha-\\sin ^{2} \\alpha\\\\=   \\frac{1-\\tan ^{2} \\alpha}{1+\\tan ^{2} \\alpha}=-\\frac{3}{5} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u5df2\u77e5\u89d2  \\alpha, \\beta  \u6ee1\u8db3  \\tan \\alpha=\\frac{1}{3}, 2 \\sin \\beta=\\sin (2 \\alpha+\\beta) , \u6c42  \\tan \\beta.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-frac-1-2-tan-alpha-frac-1-3-rightarrow-sin2-alpha-frac-3-5-cos2-alpha-frac-4-5-2-sin-beta-sin-2-alpha-beta-tan-beta-frac-1-2\"><pre>\u7b54\u6848\uff1a\\frac{1}{2} ;\u63d0\u793a\uff1a\\tan \\alpha=\\frac{1}{3}, \\Rightarrow \\sin2 \\alpha=\\frac{3}{5},\\cos2 \\alpha=\\frac{4}{5},\u539f\u5f0f~2 \\sin \\beta=\\sin (2 \\alpha+\\beta)~~~~~~~~\\\\\n\u5c55\u5f00\u4ee3\u5165\u5f97 \\tan \\beta=\\frac{1}{2}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u82e5  \\alpha  \u4e3a\u9510\u89d2,  \\tan \\alpha=\\frac{1}{\\cos 2 \\alpha+1} , \u5219  \\tan \\alpha=(\\quad) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\A.  \\frac{1}{2} ~~\nB. 1~~\nC.  2-\\sqrt{3} ~~\nD.  \\sqrt{3} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-b-tan-alpha-frac-sin-2-alpha-cos-2-alpha-2-cos-2-alpha-frac-tan-2-alpha-1-2-tan-2-alpha-2-tan-alpha-1-0-tan-alpha-1\"><pre>\u7b54\u6848 :B;\u63d0\u793a\uff1a\n \\tan \\alpha=\\frac{\\sin ^{2} \\alpha+\\cos ^{2} \\alpha}{2 \\cos ^{2} \\alpha}=\\frac{ \\tan ^{2} \\alpha+1}{2}\n,\u5373  \\tan ^{2} \\alpha-2 \\tan \\alpha+1=0 , ~~~~~~\\\\\u89e3\u5f97  \\tan \\alpha=1 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.\u5df2\u77e5  \\theta \\in(0, \\pi), \\sin \\theta+\\cos \\theta=\\frac{1}{5} , \u6c42\u503c(1)\\sin \\theta-\\cos \\theta; (2)\\sin \\theta;(3)\\cos \\theta;(4)\\tan \\theta.~~~~~~~\\\\\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-sin-theta-cos-theta-frac-7-5-2-sin-theta-frac-4-5-3-cos-theta-frac-3-5-4-tan-theta-frac-4-3-sin-theta-cos-theta-frac-1-5-2-sin-theta-cos-theta-frac-24-25-lt-0-because-theta-in-0-pi-therefore-frac-pi-2-lt-theta-lt-pi-quad-therefore-sin-theta-cos-theta-gt-0-quad-therefore-sin-theta-cos-theta-sqrt-1-2-sin-theta-cos-theta-frac-7-5-sin-theta-frac-4-5-cos-theta-frac-3-5-therefore-tan-theta-frac-4-3\"><pre>\u7b54\u6848:(1) \\sin \\theta-\\cos \\theta=\\frac{7}{5};(2) \\sin \\theta=\\frac{4}{5} ;\n(3)\\cos \\theta=-\\frac{3}{5} ;\n(4)\\tan \\theta=-\\frac{4}{3} .~~~~~~~~~~~~~~~~~~~~~~~\\\\\u63d0\u793a\uff1a\u7531\u9898\u610f\u77e5  \\sin \\theta+\\cos \\theta=\\frac{1}{5}, \u5e73\u65b9\u5f97 2 \\sin \\theta \\cos \\theta=-\\frac{24}{25}&lt;0 , \u53c8  \\because \\theta \\in(0, \\pi), ~~~~~~~~~\\\\\\therefore \\frac{\\pi}{2}&lt; \n \\theta&lt;\\pi, \\quad \\therefore \\sin \\theta-\\cos \\theta&gt;0, \\quad \\therefore \\sin \\theta-\\cos \\theta=\\sqrt{1-2 \\sin \\theta \\cos \\theta}=\\frac{7}{5}, ~~~~~~~~~~~~~~\\\\\u4e0e\u5df2\u77e5\u8054\u7acb\uff0c \\sin \\theta=\\frac{4}{5}, \\cos \\theta=-\\frac{3}{5} .\n \\therefore \\tan \\theta=-\\frac{4}{3}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.\u5df2\u77e5  -\\pi &lt; x &lt; 0, \\sin (\\pi+x)-\\cos x=-\\frac{1}{5} , \u6c42  \\frac{\\sin 2 x+2 \\sin ^{2} x}{1-\\tan x}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-frac-24-175-rightarrow-sin-x-cos-x-frac-1-5-rightarrow-2-sin-x-cos-x-frac-24-25-rightarrow-sin-x-cos-x-2-1-2-sin-x-cos-x-frac-49-25-rightarrow-frac-pi-2-lt-x-lt-0-rightarrow-sin-x-cos-x-frac-7-5-rightarrow-sin-x-frac-3-5-cos-x-frac-4-5-tan-x-frac-3-4\"><pre>\u7b54\u6848\uff1a  -\\frac{24}{175} ;\u63d0\u793a\uff1a\n\u7531\u5df2\u77e5\\Rightarrow  \\sin x+\\cos x=\\frac{1}{5}, \\Rightarrow 2 \\sin x \\cos x=-\\frac{24}{25} ,\\Rightarrow~~~~~~~~~~~~~~~~~\\\\(\\sin x-\\cos x)^{2}=1-2 \\sin x \\cos x   =\\frac{49}{25} , \u7f29\u5c0f\u89d2\u7684\u8303\u56f4\\Rightarrow  -\\frac{\\pi}{2}&lt; x&lt; 0    \\Rightarrow ~~~~~~~~~~~~~~~~~~~~~~\\\\\\sin x-\\cos x=-\\frac{7}{5} ,\\Rightarrow\\sin x =-\\frac{3}{5},\\cos x=\\frac{4}{5},\\tan x=-\\frac{3}{4}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>7.\u5316\u7b80\\frac{\\sin (2 \\pi-\\alpha) \\cos (\\pi+\\alpha) \\cos \\left(\\displaystyle\\frac{\\pi}{2}+\\alpha\\right) \\cos \\left(\\displaystyle\\frac{11 \\pi}{2}-\\alpha\\right)}{\\cos (\\pi-\\alpha) \\sin (3 \\pi-\\alpha) \\sin (-\\pi-\\alpha) \\sin \\left(\\displaystyle\\frac{9 \\pi}{2}+\\alpha\\right)}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-d1111\"><pre>\u7b54\u6848:-\\tan \\alpha;\u63d0\u793a\uff1a\u5316\u7b80\u4e3a\\frac{(-\\sin \\alpha)(-\\cos \\alpha)(- \\sin\\alpha) (-\\sin \\alpha)}{(-\\cos \\alpha)\\sin \\alpha\\sin \\alpha\\cos \\alpha}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>8.\u6c42\u503c:(1)\\frac{1}{\\sin 10^{\\circ}}-\\frac{\\sqrt{3}}{\\sin 80^{\\circ}};(2)\\sin 40^{\\circ}\\left(\\tan 10^{\\circ}-\\sqrt{3}\\right); (3)\\frac{2 \\cos 58^{\\circ}+\\sin 28^{\\circ}}{\\cos 28^{\\circ}};~~~~~~~~~~~~~\\\\ \n\n\n<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(4)   \\frac{\\sin ^{2} 35^{\\circ}-\\displaystyle\\frac{1}{2}}{\\cos 10^{\\circ} \\cdot \\cos 80^{\\circ}}; (5)2 \\sqrt{1+\\sin 4}+\\sqrt{2+2 \\cos 4}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-4-frac-cos-10-circ-sqrt-3-sin-10-circ-sin-10-circ-cos-10-circ-frac-2-left-frac-1-2-cos-10-circ-frac-sqrt-3-2-sin-10-circ-right-sin-10-circ-cos-10-circ-frac-4-sin-left-30-circ-10-circ-right-sin-20-circ-4\"><pre>\u7b54\u6848 (1)4; \u63d0\u793a:\u539f\u5f0f  =\\frac{\\cos 10^{\\circ}-\\sqrt{3} \\sin 10^{\\circ}}{\\sin 10^{\\circ} \\cos 10^{\\circ}}=   \\frac{4 \\sin \\left(30^{\\circ}-10^{\\circ}\\right)}{\\sin 20^{\\circ}}=4 ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-2-2-sin-40-circ-cdot-left-frac-sin-10-circ-cos-10-circ-sqrt-3-right-sin-40-circ-cdot-frac-sin-10-circ-sqrt-3-cos-10-circ-cos-10-circ-sin-40-circ-cdot-frac-2-sin-50-circ-cos-10-circ-frac-2-sin-40-circ-cdot-cos-40-circ-cos-10-circ-frac-sin-80-circ-cos-10-circ-1\"><pre>(2)-1; \u63d0\u793a\uff1a\\sin 40^{\\circ} \\cdot\\left(\\frac{\\sin 10^{\\circ}}{\\cos 10^{\\circ}}-\\sqrt{3}\\right)=\\sin 40^{\\circ} \\cdot \\frac{\\sin 10^{\\circ}-\\sqrt{3} \\cos 10^{\\circ}}{\\cos 10^{\\circ}} ~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n\n=\\sin 40^{\\circ} \\cdot \\frac{-2 \\sin 50^{\\circ}}{\\cos 10^{\\circ}}=\\frac{-2 \\sin 40^{\\circ} \\cdot \\cos 40^{\\circ}}{\\cos 10^{\\circ}}=\\frac{-\\sin 80^{\\circ}}{\\cos 10^{\\circ}}=-1 ;<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-3-sqrt-3-frac-2-cos-left-30-circ-28-circ-right-sin-28-circ-cos-28-circ-frac-sqrt-3-cos-28-circ-cos-28-circ-sqrt-3\"><pre>(3)\\sqrt{3}; \n\u63d0\u793a:\u539f\u5f0f  =\\frac{2 \\cos \\left(30^{\\circ}+28^{\\circ}\\right)+\\sin 28^{\\circ}}{\\cos 28^{\\circ}}=\\frac{\\sqrt{3} \\cos 28^{\\circ}}{\\cos 28^{\\circ}}=\\sqrt{3} ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-4-1-frac-displaystyle-frac-1-cos-70-circ-2-frac-1-2-cos-10-circ-cdot-sin-10-circ-frac-cos-70-circ-2-sin-10-circ-cdot-cos-10-circ-frac-sin-20-circ-sin-20-circ-1\"><pre>(4)-1;\u539f\u5f0f=\\frac{\\displaystyle\\frac{1-\\cos 70^{\\circ}}{2}-\\frac{1}{2}}{\\cos 10^{\\circ} \\cdot \\sin 10^{\\circ}} \n =-\\frac{\\cos 70^{\\circ}}{2 \\sin 10^{\\circ} \\cdot \\cos 10^{\\circ}}=-\\frac{\\sin 20^{\\circ}}{\\sin 20^{\\circ}}=-1 .~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-2-sqrt-sin-2-cos-2-2-sqrt-4-cos-2-2-2-sin-2-cos-2-2-cos-2-2-sin-2-cos-2-2-cos-2-2-sin-2\"><pre>(5)2 \\sin 2;\u539f\u5f0f=2 \\sqrt{(\\sin 2+\\cos 2)^{2}}+\\sqrt{4 \\cos ^{2} 2} \n=2|\\sin 2+\\cos 2|+2|\\cos 2|~~~~~~~~~~~~~~~~~\\\\=2(\\sin 2+\\cos 2)-2 \\cos 2=2 \\sin 2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>9.(1) \u82e5  \\alpha+\\beta=-\\frac{3 \\pi}{4} , \u6c42  (1+\\tan \\alpha)(1+\\tan \\beta);~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2)\u6c42 \\left(1+\\tan 13^{\\circ}\\right)\\left(1+\\tan 17^{\\circ}\\right)\\left(1+\\tan 28^{\\circ}\\right) \\cdot\\left(1+\\tan 32^{\\circ}\\right).~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-111111111111111111111111\"><pre>(1)\u7b54\u6848:2;\u63d0\u793a\uff1a \\boldsymbol{\\operatorname { t a n }}(\\alpha+\\beta)=\\frac{\\boldsymbol{\\operatorname { t a n }} \\alpha+\\tan \\beta}{1-\\boldsymbol{\\operatorname { t a n }} \\alpha \\boldsymbol{\\operatorname { t a n }} \\beta}=1 ,\n\\therefore  1-\\tan \\alpha \\boldsymbol{\\operatorname { t a n }} \\beta=\\tan \\alpha+\\tan \\beta ,\n\\\\\u5219 (1+\\tan \\alpha) \\cdot(1+\\tan \\beta)=1+\\tan \\alpha+\\tan \\beta+\\tan \\alpha \\boldsymbol{\\operatorname { t a n }} \\beta=2 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(2)\u7b54\u6848:4;\u63d0\u793a:\u540c(1),\\left(1+\\tan 13^{\\circ}\\right)\\left(1+\\tan 32^{\\circ}\\right)=\\left(1+\\tan 17^{\\circ}\\right)\\left(1+\\tan 28^{\\circ}\\right)=2\n.~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>10.\u5c06\u4e0b\u5217\u51fd\u6570\u5316\u7b80\u4e3ay=A\\sin(\\omega x+\\varphi )+b\u7684\u5f62\u5f0f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(1)f(x)=2\\sin^2\\omega x+2\\sqrt{3}\\sin\\omega x\\cos\\omega x-1;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2)f(x)=(1-\\sqrt{3}) \\cos ^{2} x+\\sin x \\cos x+\\sin \\left(x+\\frac{\\pi}{4}\\right) \\sin \\left(x-\\frac{\\pi}{4}\\right) ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(3) f(x)=\\sin \\left(2 \\omega x-\\frac{\\pi}{6}\\right)-2 \\cos ^{2} \\omega x+1 ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(4) f(x)=\\cos ^{2}\\left(x+\\frac{\\pi}{6}\\right)+\\frac{\\sqrt{3}}{2} \\sin 2 x ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(5)f(x)=\\sin \\omega x \\sin \\left(\\omega x+\\frac{\\pi}{3}\\right)-\\sin ^{2} \\omega x ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(6)f(x)=\\cos ^{4} x-2 \\sin x \\cdot \\cos x-\\sin ^{4} x;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(7)f(x)=\\sin ^{2}\\left(\\frac{\\pi}{2}+x\\right)+\\sqrt{3} \\sin (\\pi-x) \\cos x-\\cos 2 x .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-da1\"><pre>\u7b54\u6848:(1)  f(x)=2 \\sin \\left(x-\\frac{\\pi}{6}\\right);~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2)f(x)=\\sin \\left(2 x-\\frac{\\pi}{3}\\right)+\\frac{1-\\sqrt{3}}{2};~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n (3) f(x)=\\sqrt{3} \\sin \\left(2 \\omega x-\\frac{\\pi}{3}\\right) ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(4)f(x)=\\frac{1}{2} \\sin \\left(2 x+\\frac{\\pi}{6}\\right)+\\frac{1}{2} ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(5)f(x)=\\frac{1}{2} \\sin \\left(2 \\omega x+\\frac{\\pi}{6}\\right)-\\frac{1}{4};~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(6)f(x)=\\cos 2 x-\\sin 2 x=-\\sqrt{2} \\sin \\left(2 x-\\frac{\\pi}{4}\\right);~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(7)f(x)=\\sin \\left(2 x-\\frac{\\pi}{6}\\right)+\\frac{1}{2}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-sin-2-omega-x-frac-1-cos-2-omega-x-2-rightarrow-f-x-cos-2-omega-x-sqrt-3-sin-2-omega-x-2-sin-left-2-omega-x-frac-pi-6-right-2-f-x-1-sqrt-3-frac-1-cos-2-x-2-frac-1-2-sin-2-x-frac-1-2-left-sin-2-x-cos-2-x-right-frac-1-sqrt-3-2-frac-sqrt-3-cos-2-x-2-frac-1-2-sin-2-x-sin-left-2-x-frac-pi-3-right-frac-1-sqrt-3-2-3-f-x-frac-sqrt-3-2-sin-2-omega-x-frac-1-2-cos-2-omega-x-cos-2-omega-x-sqrt-3-left-frac-1-2-sin-2-omega-x-frac-sqrt-3-2-cos-2-omega-x-right-sqrt-3-sin-left-2-omega-x-frac-pi-3-right-4-f-x-cos-2-left-x-frac-pi-6-right-frac-sqrt-3-2-sin-2-x-frac-1-cos-left-2-x-frac-pi-3-right-2-frac-sqrt-3-2-sin-2-x-frac-1-2-frac-1-4-cos-2-x-frac-sqrt-3-4-sin-2-x-frac-1-2-sin-left-2-x-frac-pi-6-right-frac-1-2-5-f-x-sin-omega-x-left-sin-omega-x-cos-frac-pi-3-cos-omega-x-sin-frac-pi-3-right-sin-2-omega-x-frac-sqrt-3-2-cos-omega-x-sin-omega-x-frac-1-2-sin-2-omega-x-frac-sqrt-3-4-sin-2-omega-x-frac-1-4-1-cos-2-omega-x-frac-1-2-sin-left-2-omega-x-frac-pi-6-right-frac-1-4-6-f-x-cos-4-x-sin-4-x-2-sin-x-cdot-cos-x-left-cos-2-x-sin-2-x-right-left-cos-2-x-sin-2-x-right-sin-2-x-cos-2-x-sin-2-x-sqrt-2-sin-left-2-x-frac-pi-4-right-7-f-x-frac-1-cos-2-x-2-frac-sqrt-3-2-sin-2-x-cos-2-x-frac-sqrt-3-2-sin-2-x-frac-1-2-cos-2-x-frac-1-2-sin-left-2-x-frac-pi-6-right-frac-1-2\"><pre>(1)\u63d0\u793a:  \u964d\u5e42\u516c\u5f0f  \\sin ^{2} \\omega x=\\frac{1-\\cos 2 \\omega x}{2} \\Rightarrow f(x)=-\\cos 2 \\omega x+   \\sqrt{3} \\sin 2 \\omega x~~~~~~~~~~~~~~~~~\\\\=2 \\sin \\left(2 \\omega x-\\frac{\\pi}{6}\\right) ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2)\u63d0\u793a:f(x)  =(1-\\sqrt{3}) \\frac{1+\\cos 2 x}{2}+\\frac{1}{2} \\sin 2 x+\\frac{1}{2}\\left(\\sin ^{2} x-\\cos ^{2} x\\right) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n\n=\\frac{1-\\sqrt{3}}{2}-\\frac{\\sqrt{3} \\cos 2 x}{2}+\\frac{1}{2} \\sin 2 x=\\sin \\left(2 x-\\frac{\\pi}{3}\\right)+\\frac{1-\\sqrt{3}}{2};~~~~~~~~\\\\\n(3) \u63d0\u793a:f(x)  =\\frac{\\sqrt{3}}{2} \\sin 2 \\omega x-\\frac{1}{2} \\cos 2 \\omega x-\\cos 2 \\omega x \n\n=\\sqrt{3}\\left(\\frac{1}{2} \\sin 2 \\omega x-\\frac{\\sqrt{3}}{2} \\cos 2 \\omega x\\right)~\\\\=\\sqrt{3} \\sin \\left(2 \\omega x-\\frac{\\pi}{3}\\right);~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n\\\\\n(4)\u63d0\u793a: f(x)=\\cos ^{2}\\left(x+\\frac{\\pi}{6}\\right)+\\frac{\\sqrt{3}}{2} \\sin 2 x=\\frac{1+\\cos \\left(2 x+\\frac{\\pi}{3}\\right)}{2}+\\frac{\\sqrt{3}}{2} \\sin 2 x ~~~~~~~~~~~~~~~~~~\\\\\n\n=\\frac{1}{2}+\\frac{1}{4} \\cos 2 x+\\frac{\\sqrt{3}}{4} \\sin 2 x=\\frac{1}{2} \\sin \\left(2 x+\\frac{\\pi}{6}\\right)+\\frac{1}{2} ;~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(5)\u63d0\u793a:\nf(x)=\\sin \\omega x\\left(\\sin \\omega x \\cos \\frac{\\pi}{3}+\\cos \\omega x \\sin \\frac{\\pi}{3}\\right)-\\sin ^{2} \\omega x=\\frac{\\sqrt{3}}{2} \\cos \\omega x \\sin \\omega x-~\\\\\\frac{1}{2} \\sin ^{2} \\omega x \n=\\frac{\\sqrt{3}}{4} \\sin 2 \\omega x-\\frac{1}{4}(1-\\cos 2 \\omega x)=\\frac{1}{2} \\sin \\left(2 \\omega x+\\frac{\\pi}{6}\\right)-\\frac{1}{4};\n\\\\\n(6)\u63d0\u793a: f(x)=\\cos ^{4} x-\\sin ^{4} x-2 \\sin x \\cdot \\cos x=\\left(\\cos ^{2} x-\\sin ^{2} x\\right)\\left(\\cos ^{2} x+\\sin ^{2} x\\right)-~~\\\\\\sin 2 x \n=\\cos 2 x-\\sin 2 x=-\\sqrt{2} \\sin \\left(2 x-\\frac{\\pi}{4}\\right);~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(7)\u63d0\u793a: f(x)=\\frac{1+\\cos 2 x}{2}+\\frac{\\sqrt{3}}{2} \\sin 2 x-\\cos 2 x=\\frac{\\sqrt{3}}{2} \\sin 2 x-\\frac{1}{2} \\cos 2 x+\\frac{1}{2} ~~~~~~~~~~~~~~~\\\\\n=\\sin \\left(2 x-\\frac{\\pi}{6}\\right)+\\frac{1}{2}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1111111111111111111111111111\"><pre><\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-c71bbb6\" data-block-id=\"c71bbb6\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-1111111111111111\">\u7528\u5df2\u77e5\u89d2\u8868\u793a\u6240\u6c42\u89d2<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.(1)\u5df2\u77e5  \\alpha  \u4e3a\u9510\u89d2, \u4e14  \\cos \\left(\\alpha+\\frac{\\pi}{6}\\right)=\\frac{5}{13} , \u6c42 \\cos \\alpha  \u7684\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\\\\(2)\u82e5\\sin (\\theta +\\frac{\\pi}{6})=\\frac{1}{3},\\theta\\in(0,\\pi)\uff0c\u6c42\\cos\\theta\u7684\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-d\"><pre>\u7b54\u6848\uff1a\\frac{5 \\sqrt{3}+12}{26} \uff1b\u63d0\u793a\uff1a\\therefore \\cos \\alpha=\\cos \\left[\\left(\\alpha+\\frac{\\pi}{6}\\right)-\\frac{\\pi}{6}\\right],\u5176\u4e2d\uff0c\\sin \\left(\\alpha+\\frac{\\pi}{6}\\right)=\\frac{12}{13} .~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-11111111111111111111111111\"><pre>(2)\u7b54\u6848:\\frac{1-2\\sqrt{6}}{6};\u63d0\u793a: \\cos \\theta=\\cos \\left[\\left(\\theta+\\frac{\\pi}{6}\\right)-\\frac{\\pi}{6}\\right],\u5176\u4e2d\uff0c\\because \\theta\\in(0,\\pi),\\therefore \\theta+\\frac{\\pi}{6}\\in\\\\ (\\frac{\\pi}{6},\\frac{7\\pi}{6})\\sin\\frac{\\pi}{6}=\\frac{1}{2}&gt;\\sin (\\theta +\\frac{\\pi}{6})=\\frac{1}{3},\\therefore \\theta +\\frac{\\pi}{6}\u4e0d\u80fd\u662f\u9510\u89d2,\\cos(\\theta +\\frac{\\pi}{6})=-\\frac{2\\sqrt{2}}{3}.~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u5df2\u77e5  \\sin \\alpha=\\frac{2 \\sqrt{5}}{5}, \\sin (\\beta-\\alpha)=-\\frac{\\sqrt{10}}{10}, \\alpha, \\beta  \u5747\u4e3a\u9510\u89d2, \u5219  \\beta  \u7b49\u4e8e (~~ )~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.  \\frac{5 \\pi}{12} ~~\nB.  \\frac{\\pi}{3} ~~\n \\mathrm{C} \\frac{\\pi}{4} ~~\nD.  \\frac{\\pi}{6} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-d1\"><pre>\u7b54\u6848:C;\u63d0\u793a: \\sin \\beta=\\sin [\\alpha+(\\beta-\\alpha)]=\\sin \\alpha \\cdot \\cos (\\beta-\\alpha)+\\cos \\alpha \\cdot \\sin (\\beta-\\alpha), \\alpha, \\beta ~~ \\\\\u5747\u4e3a\u9510\u89d2, \u6240\u4ee5  \\cos \\alpha=\\frac{\\sqrt{5}}{5}, \\cos (\\beta-\\alpha)=\\frac{3 \\sqrt{10}}{10} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u5df2\u77e5  \\alpha, \\beta \\in\\left(\\frac{3 \\pi}{4}, \\pi\\right), \\sin (\\alpha+\\beta)=-\\frac{3}{5}, \\sin \\left(\\beta-\\frac{\\pi}{4}\\right)=\\frac{24}{25} , \u6c42  \\cos \\left(\\alpha+\\frac{\\pi}{4}\\right).~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-d11\"><pre>\u7b54\u6848\uff1a-\\frac{4}{5} ;\u63d0\u793a\uff1a \\cos \\left(\\alpha+\\frac{\\pi}{4}\\right)=\\cos \\left[(\\alpha+\\beta)-\\left(\\beta-\\frac{\\pi}{4}\\right)\\right],\u5176\u4e2d,\\because \\alpha+\\beta \\in~~~~~~~~~~~~~~\\\\\n\\left(\\frac{3 \\pi}{2}, 2 \\pi\\right) , \\therefore   \\cos (\\alpha+\\beta)=\\frac{4}{5}; \\because  \\beta-\\frac{\\pi}{4} \\in\\left(\\frac{\\pi}{2}, \\frac{3 \\pi}{4}\\right) ,\\therefore  \\cos \\left(\\beta-\\frac{\\pi}{4}\\right)=-\\frac{7}{25} .~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4. \u5df2\u77e5  \\cos \\left(\\theta+\\frac{\\pi}{4}\\right)=\\frac{\\sqrt{10}}{10}, \\theta \\in\\left(0, \\frac{\\pi}{2}\\right) , \u6c42  \\sin \\left(2 \\theta-\\frac{\\pi}{3}\\right).~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-d111\"><pre>\u7b54\u6848\uff1a\\frac{4-3 \\sqrt{3}}{10} ;\u63d0\u793a:\u4ee4t=\\theta+\\frac{\\pi}{4},\u5219\\cos t=\\frac{\\sqrt{10}}{10}\u4e14t \\in \\left ( \\frac{\\pi}{4}, \\frac{3\\pi}{4} \\right ) ,\\theta =t- \\frac{\\pi}{4}, ~~~~~~~~~~~~\\\\\u5219\\sin \\left(2 \\theta-\\frac{\\pi}{3}\\right)= \\sin \\left(2 t-\\frac{2\\pi}{3}\\right),\u5176\u4e2d\\sin 2t=\\frac{3}{5},\\cos 2t=-\\frac{4}{5}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u53d8\u5f0f1. \u5df2\u77e5  \\alpha  \u4e3a\u9510\u89d2,  \\cos \\left(\\alpha+\\frac{\\pi}{6}\\right)=\\frac{4}{5} , \u6c42  \\sin \\left(2 \\alpha+\\frac{\\pi}{12}\\right).~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111111111111111111111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-da\"><pre>\u7b54\u6848:\\frac{7\\sqrt{2} }{50} ;\u63d0\u793a\uff1a\u4ee4\\alpha +\\frac{\\pi }{6} =t,\u5219\\cos t=\\frac{4}{5} ,\\sin t=\\frac{3}{5}, \\sin \\left(2 \\alpha+\\frac{\\pi}{12}\\right)=\\sin (2t-\\frac{\\pi }{4} ) ~~\\\\=\\frac{\\sqrt{2} }{2} (\\sin 2t-\\cos 2t)=\\frac{7\\sqrt{2} }{50}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u53d8\u5f0f2.\u82e5  \\cos \\left(\\frac{\\pi}{3}-2 x\\right)=-\\frac{7}{8} , \u5219  \\sin \\left(x+\\frac{\\pi}{3}\\right)  \u7684\u503c\u4e3a(\\quad)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\nA.  \\frac{1}{4} \\quad\nB.  \\frac{7}{8} \\quad\nC.  \\pm \\frac{1}{4} \\quad\nD.\\pm \\frac{7}{8} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-da11\"><pre>\u7b54\u6848:C;\u4ee4\\frac{\\pi}{3}-2 x=t,\\cos t=-\\frac{7}{8}, \\sin \\left(x+\\frac{\\pi}{3}\\right) =\\cos \\frac{t}{2}=\\pm \\frac{1}{4}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.\u5df2\u77e5  \\sin \\left(\\frac{\\pi}{3}-x\\right)=\\frac{1}{3} ,   0&lt; x&lt; \\frac{\\pi}{6} , \u6c42  \\sin \\left(\\frac{\\pi}{6}+x\\right)-\\cos \\left(\\frac{2 \\pi}{3}+x\\right)  \u7684\u503c.~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-frac-4-sqrt-2-3-frac-pi-3-x-t-x-frac-pi-3-t-quad-therefore-frac-pi-6-t-frac-pi-3-therefore-sin-t-frac-1-3\"><pre>\u7b54\u6848:  \\frac{4 \\sqrt{2}}{3} ;\n\u63d0\u793a\uff1a\u4ee4  \\frac{\\pi}{3}-x=t,  \\therefore \\frac{\\pi}{6} &lt; t&lt;\\frac{\\pi}{3}, \u4e14 x=\\frac{\\pi}{3}-t\\therefore \\sin t=\\frac{1}{3} \uff0c\u65b9\u6cd5\u540c\u4e0a.~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n \n","protected":false},"excerpt":{"rendered":"<p>\u4e09\u89d2\u51fd\u6570\u6982\u5ff5\u53ca\u6027\u8d28<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-2915","post","type-post","status-publish","format-standard","hentry","category-2"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/2915","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2915"}],"version-history":[{"count":0,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/2915\/revisions"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2915"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}