{"id":17429,"date":"2010-12-07T11:55:28","date_gmt":"2010-12-07T03:55:28","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=17429"},"modified":"2021-10-06T16:30:21","modified_gmt":"2021-10-06T08:30:21","slug":"%e5%bb%a3%e7%be%a9%e8%a7%92%e7%9a%84%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b8the-trigonometric-functions-of-a-generalized-angle","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%bb%a3%e7%be%a9%e8%a7%92%e7%9a%84%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b8the-trigonometric-functions-of-a-generalized-angle\/","title":{"rendered":"\u5ee3\u7fa9\u89d2\u7684\u4e09\u89d2\u51fd\u6578"},"content":{"rendered":"

\u5ee3\u7fa9\u89d2\u7684\u4e09\u89d2\u51fd\u6578 (The Trigonometric Functions of a Generalized Angle) <\/span>
\n\u570b\u7acb\u5c4f\u6771\u9ad8\u7d1a\u4e2d\u5b78\u6578\u5b78\u79d1\u694a\u74ca\u8339\u8001\u5e2b \/ \u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u5b78\u7cfb\u6d2a\u842c\u751f\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u6211\u5011\u5c0d\u89d2\u5ea6\u7684\u6982\u5ff5\uff0c\u9664\u4e86\u92b3\u89d2\uff08\\(0^\\circ<\\theta<90^\\circ\\)\uff09\u4e4b\u5916\uff0c\u7576\u7136\u9084\u6709\u5927\u6216\u7b49\u65bc \\(90^\\circ\\) \u7684\u89d2\u5ea6\uff0c\u4f8b\u5982\uff1a\u6642\u91dd\u7684\u65cb\u8f49\u3001\u8eca\u8f2a\u7684\u8f49\u52d5\u3001\u5730\u7403\u7684\u516c\u8f49\u2026<\/strong>\u7b49\u666e\u904d\u5b58\u5728\u751f\u6d3b\u4e2d\u7684\u8f49\u52d5\u73fe\u8c61\u3002\u6240\u4ee5\uff0c\u539f\u5148\u5b9a\u7fa9\u5728\u92b3\u89d2\uff08\\(0^\\circ<\\theta<90^\\circ\\)\uff09\u689d\u4ef6\u4e0b\u7684\u4e09\u89d2\u51fd\u6578\uff0c\u986f\u7136\u7121\u6cd5\u6db5\u84cb\u65cb\u8f49\u73fe\u8c61\u6240\u6d89\u53ca\u7684\u89d2\u5ea6\u7bc4\u570d\u3002\u4f46\u662f\uff0c\u5982\u4f55\u4ee5\u66f4\u5bec\u5ee3\u7684\u89d2\u5ea6\u4f86\u62d3\u5c55\u92b3\u89d2\u4e09\u89d2\u51fd\u6578\u7684\u5b9a\u7fa9\u5462\uff1f\u9019\u500b\u554f\u984c\u78ba\u5be6\u8b93\u6578\u5b78\u5bb6\u50b7\u900f\u8166\u7b4b\uff0c\u89e3\u6c7a\u4e4b\u9053\u6b63\u662f\u76f4\u89d2\u5ea7\u6a19\u7cfb\u7d71\uff01\u5ef6\u62d3\u7684\u5b9a\u7fa9\u5982\u4e0b\uff1a<\/p>\n

\u5ea7\u6a19\u5e73\u9762\u4e0a\uff0c\u8a2d \\(O\\) \u70ba\u539f\u9ede\uff0c\\(\\theta\\) \u70ba\u6a19\u6e96\u4f4d\u7f6e\u89d2\uff0c\u5728 \\(\\theta\\) \u7684\u7d42\u908a\u4e0a\u4efb\u53d6\u4e00\u9ede \\(P(x,y)\\)\uff0c\uff08\\(P\\) \u4e0d\u662f\u539f\u9ede\uff09\uff0c\u6b64\u6642 \\(xy\\neq{0}\\)\uff0c\u4ee4 \\(\\overline{OP}=r=\\sqrt{x^2+y^2}\\)\uff0c\u5ee3\u7fa9\u89d2\u7684\u4e09\u89d2\u51fd\u6578\u70ba\uff1a<\/p>\n

\"\"<\/a><\/p>\n

\u5ee3\u7fa9\u4e09\u89d2\u51fd\u6578\u7684\u5b9a\u7fa9\u8207\u92b3\u89d2\u4e09\u89d2\u51fd\u6578\u7684\u5b9a\u7fa9\u662f\u76f8\u7b26\u4e00\u81f4\u7684\u3002\u6b64\u5916\uff0c\u5ee3\u7fa9\u89d2\u7684\u4e09\u89d2\u51fd\u6578\u503c\u53ea\u548c\u7d42\u908a\u7684\u4f4d\u7f6e\u6709\u95dc\uff0c\u5373\u540c\u754c\u89d2\u7684\u4e09\u89d2\u51fd\u6578\u503c\u76f8\u7b49\u3002\u5982\u679c \\(\\theta\\) \u7684\u7d42\u908a\u843d\u5728\u7b2c\u4e00\u3001\u4e8c\u3001\u4e09\u6216\u56db\u8c61\u9650\uff0c\u5247\u5206\u5225\u7a31 \\(\\theta\\) \u70ba\u7b2c\u4e00\u3001\u4e8c\u3001\u4e09\u6216\u56db\u8c61\u9650\u89d2\uff0c\u5982\u4e0a\u8ff0\u7684\u56db\u500b\u5716\u5f62\u3002<\/p>\n

\u7279\u5225\u6ce8\u610f\u7684\u662f\uff0c\u9019\u4e9b\u5b9a\u7fa9\u7684\u6bd4\u503c\u53ea\u6709\u5728\u5206\u6bcd\u4e0d\u70ba \\(0\\) \u7684\u60c5\u6cc1\u4e0b\u624d\u6709\u610f\u7fa9\u3002\u81f3\u65bc \\(0^\\circ,90^\\circ,180^\\circ,270^\\circ\\) \u9019\u4e9b\u4e0d\u5c6c\u65bc\u4efb\u4f55\u8c61\u9650\u7684\u89d2\uff0c\u4e09\u89d2\u51fd\u6578\u503c\u53c8\u662f\u5982\u4f55\u5462\uff1f\u4e00\u6a23\u53ef\u4ee5\u5728 \\(\\theta\\) \u7684\u7d42\u908a\u4e0a\u4efb\u53d6\u4e00\u9ede \\(P(x,y)\\)\uff0c\u82e5\u662f \\(\\theta\\) \u7684\u7d42\u908a\u843d\u5728 \\(y\\) \u8ef8\u4e0a\uff0c\u5247 \\(P\\) \u9ede\u7684 \\(x\\) \u5750\u6a19\u70ba \\(0\\)\uff0c\u6240\u4ee5 \\(\\tan\\theta\\) \u8207 \\(\\sec\\theta\\) \u7121\u610f\u7fa9\uff1b\u82e5\u662f \\(\\theta\\) \u7684\u7d42\u908a\u843d\u5728 \\(x\\) \u8ef8\u4e0a\uff0c\u5247 \\(P\\) \u9ede\u7684 \\(y\\) \u5750\u6a19\u70ba \\(0\\)\uff0c\u6b64\u6642 \\(\\cot\\theta\\) \u8207 \\(\\csc\\theta\\) \u7121\u610f\u7fa9\u3002<\/p>\n

\"\"<\/span><\/a><\/p>\n

\u9032\u4e00\u6b65\u4f86\u8aaa\uff0c\u5ee3\u7fa9\u89d2 \\(\\theta\\)\u00a0\u7684\u4e09\u89d2\u51fd\u6578\u503c\u662f\u7531\u9ede \\(P(x,y)\\) \u548c \\(r\\) \u6c7a\u5b9a\uff0c\\(x\\) \u548c \\(y\\) \u53ef\u6b63\u53ef\u8ca0\uff0c\u4f46 \\(r\\) \u6046\u6b63\uff0c\u6240\u4ee5 \\(x\\) \u548c \\(y\\) \u7684\u6b63\u8ca0\u865f\u6c7a\u5b9a\u4e09\u89d2\u51fd\u6578\u503c\u7684\u6b63\u8ca0\u865f\uff0c\u5404\u8c61\u9650\u89d2\u7684\u4e09\u89d2\u51fd\u6578\u503c\u4e4b\u6b63\u8ca0\u865f\u6574\u7406\u5982\u4e0b\uff1a<\/p>\n

\"\"<\/span><\/a><\/p>\n

\u82e5\u5c07\u8868\u683c\u5167\u5bb9\u518d\u7c21\u5316\uff0c\u53ea\u6a19\u51fa\u4e09\u89d2\u51fd\u6578\u503c\u662f\u6b63\u7684\uff0c\u5247\u5f97\u5230\u53f3\u4e0a\u5716\u3002<\/p>\n

\u7e3d\u7d50\u4f86\u8aaa\uff0c\u5ea7\u6a19\u5316\u7684\u60f3\u6cd5\u6210\u529f\u5730\u5c07\u92b3\u89d2\u64f4\u5c55\u81f3\u5ee3\u7fa9\u89d2\u3001\u92b3\u89d2\u4e09\u89d2\u51fd\u6578\u5ef6\u62d3\u81f3\u5ee3\u7fa9\u89d2\u7684\u4e09\u89d2\u51fd\u6578\u3002\u540c\u6a23\u5730\uff0c\u92b3\u89d2\u4e09\u89d2\u51fd\u6578\u7684\u5404\u7a2e\u57fa\u672c\u95dc\u4fc2\uff1a\u5012\u6578\u95dc\u4fc2\u3001\u5546\u6578\u95dc\u4fc2\u3001\u5e73\u65b9\u95dc\u4fc2\u53ca\u9918\u89d2\u95dc\u4fc2\uff0c\u7531\u92b3\u89d2\u63a8\u5ee3\u5230\u5ee3\u7fa9\u89d2\u4ecd\u7136\u6210\u7acb (\u5728\u51fd\u6578\u503c\u6709\u610f\u7fa9\u4e0b)\u3002<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

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