{"id":106596,"date":"2026-06-15T17:57:43","date_gmt":"2026-06-15T09:57:43","guid":{"rendered":"https:\/\/www.dongwubaike.cn\/fanhao\/?p=106596"},"modified":"2026-06-15T17:57:43","modified_gmt":"2026-06-15T09:57:43","slug":"%e9%ab%98%e4%b8%ad%e6%95%b0%e5%ad%a6%e5%a4%8d%e4%b9%a0%e8%b5%84%e6%96%99%e6%80%bb%e7%bb%93","status":"publish","type":"post","link":"https:\/\/www.dongwubaike.cn\/fanhao\/106596.html","title":{"rendered":"\u9ad8\u4e2d\u6570\u5b66\u590d\u4e60\u8d44\u6599\u603b\u7ed3"},"content":{"rendered":"

\u6570\u5b66\u662f\u4e00\u4e2a\u7cfb\u7edf\u5316\u7684\u903b\u8f91\u4f53\u7cfb,\u5b83\u6709\u7740\u660e\u786e\u7684\u7ed3\u6784\u3002\u5728\u8fd9\u4e2a\u7ed3\u6784\u7684\u4f53\u7cfb\u4e2d,\u6570\u5b66\u77e5\u8bc6\u5177\u6709\u4e00\u5b9a\u7684\u62bd\u8c61\u6027\u548c\u5177\u4f53\u6027\u3002\u4e0b\u9762\u662f\u5c0f\u7f16\u4e3a\u5927\u5bb6\u6574\u7406\u7684\u5173\u4e8e\u9ad8\u4e2d\u6570\u5b66\u590d\u4e60\u8d44\u6599\uff0c\u5e0c\u671b\u5bf9\u60a8\u6709\u6240\u5e2e\u52a9!<\/p>\n

\u9ad8\u4e09\u6570\u5b66\u590d\u4e60\u8981\u70b9<\/strong><\/p>\n

\u4e00\u3001\u5145\u5206\u6761\u4ef6\u548c\u5fc5\u8981\u6761\u4ef6<\/p>\n

\u5f53\u547d\u9898\u201c\u82e5A\u5219B\u201d\u4e3a\u771f\u65f6\uff0cA\u79f0\u4e3aB\u7684\u5145\u5206\u6761\u4ef6\uff0cB\u79f0\u4e3aA\u7684\u5fc5\u8981\u6761\u4ef6\u3002<\/p>\n

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1.\u5b9a\u4e49\u6cd5\uff1a\u5224\u65adB\u662fA\u7684\u6761\u4ef6\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5224\u65adB=>A\u6216\u8005A=>B\u662f\u5426\u6210\u7acb\uff0c\u53ea\u8981\u628a\u9898\u76ee\u4e2d\u6240\u7ed9\u7684\u6761\u4ef6\u6309\u903b\u8f91\u5173\u7cfb\u753b\u51fa\u7bad\u5934\u793a\u610f\u56fe\uff0c\u518d\u5229\u7528\u5b9a\u4e49\u5224\u65ad\u5373\u53ef<\/p>\n

2.\u8f6c\u6362\u6cd5\uff1a\u5f53\u6240\u7ed9\u547d\u9898\u7684\u5145\u8981\u6761\u4ef6\u4e0d\u6613\u5224\u65ad\u65f6\uff0c\u53ef\u5bf9\u547d\u9898\u8fdb\u884c\u7b49\u4ef7\u88c5\u6362\uff0c\u4f8b\u5982\u6539\u7528\u5176\u9006\u5426\u547d\u9898\u8fdb\u884c\u5224\u65ad\u3002<\/p>\n

3.\u96c6\u5408\u6cd5<\/p>\n

\u5728\u547d\u9898\u7684\u6761\u4ef6\u548c\u7ed3\u8bba\u95f4\u7684\u5173\u7cfb\u5224\u65ad\u6709\u56f0\u96be\u65f6\uff0c\u53ef\u4ece\u96c6\u5408\u7684\u89d2\u5ea6\u8003\u8651\uff0c\u8bb0\u6761\u4ef6p\u3001q\u5bf9\u5e94\u7684\u96c6\u5408\u5206\u522b\u4e3aA\u3001B\uff0c\u5219\uff1a<\/p>\n

\u82e5AB\uff0c\u5219p\u662fq\u7684\u5145\u5206\u6761\u4ef6\u3002<\/p>\n

\u82e5AB\uff0c\u5219p\u662fq\u7684\u5fc5\u8981\u6761\u4ef6\u3002<\/p>\n

\u82e5A=B\uff0c\u5219p\u662fq\u7684\u5145\u8981\u6761\u4ef6\u3002<\/p>\n

\u82e5AB\uff0c\u4e14BA\uff0c\u5219p\u662fq\u7684\u65e2\u4e0d\u5145\u5206\u4e5f\u4e0d\u5fc5\u8981\u6761\u4ef6\u3002<\/p>\n

\u4e09\u3001\u77e5\u8bc6\u6269\u5c55<\/p>\n

1.\u56db\u79cd\u547d\u9898\u53cd\u6620\u51fa\u547d\u9898\u4e4b\u95f4\u7684\u5185\u5728\u8054\u7cfb\uff0c\u8981\u6ce8\u610f\u7ed3\u5408\u5b9e\u9645\u95ee\u9898\uff0c\u7406\u89e3\u5176\u5173\u7cfb(\u5c24\u5176\u662f\u4e24\u79cd\u7b49\u4ef7\u5173\u7cfb)\u7684\u4ea7\u751f\u8fc7\u7a0b\uff0c\u5173\u4e8e\u9006\u547d\u9898\u3001\u5426\u547d\u9898\u4e0e\u9006\u5426\u547d\u9898\uff0c\u4e5f\u53ef\u4ee5\u53d9\u8ff0\u4e3a\uff1a<\/p>\n

(1)\u4ea4\u6362\u547d\u9898\u7684\u6761\u4ef6\u548c\u7ed3\u8bba\uff0c\u6240\u5f97\u7684\u65b0\u547d\u9898\u5c31\u662f\u539f\u6765\u547d\u9898\u7684\u9006\u547d\u9898;<\/p>\n

(2)\u540c\u65f6\u5426\u5b9a\u547d\u9898\u7684\u6761\u4ef6\u548c\u7ed3\u8bba\uff0c\u6240\u5f97\u7684\u65b0\u547d\u9898\u5c31\u662f\u539f\u6765\u7684\u5426\u547d\u9898;<\/p>\n

(3)\u4ea4\u6362\u547d\u9898\u7684\u6761\u4ef6\u548c\u7ed3\u8bba\uff0c\u5e76\u4e14\u540c\u65f6\u5426\u5b9a\uff0c\u6240\u5f97\u7684\u65b0\u547d\u9898\u5c31\u662f\u539f\u547d\u9898\u7684\u9006\u5426\u547d\u9898\u3002<\/p>\n

2.\u7531\u4e8e\u201c\u5145\u5206\u6761\u4ef6\u4e0e\u5fc5\u8981\u6761\u4ef6\u201d\u662f\u56db\u79cd\u547d\u9898\u7684\u5173\u7cfb\u7684\u6df1\u5316\uff0c\u4ed6\u4eec\u4e4b\u95f4\u5b58\u5728\u8fd9\u5bc6\u5207\u7684\u8054\u7cfb\uff0c\u6545\u5728\u5224\u65ad\u547d\u9898\u7684\u6761\u4ef6\u7684\u5145\u8981\u6027\u65f6\uff0c\u53ef\u8003\u8651\u201c\u6b63\u96be\u5219\u53cd\u201d\u7684\u539f\u5219\uff0c\u5373\u5728\u6b63\u9762\u5224\u65ad\u8f83\u96be\u65f6\uff0c\u53ef\u8f6c\u5316\u4e3a\u5e94\u7528\u8be5\u547d\u9898\u7684\u9006\u5426\u547d\u9898\u8fdb\u884c\u5224\u65ad\u3002\u4e00\u4e2a\u7ed3\u8bba\u6210\u7acb\u7684\u5145\u5206\u6761\u4ef6\u53ef\u4ee5\u4e0d\u6b62\u4e00\u4e2a\uff0c\u5fc5\u8981\u6761\u4ef6\u4e5f\u53ef\u4ee5\u4e0d\u6b62\u4e00\u4e2a\u3002<\/p>\n

\u9ad8\u4e2d\u6570\u5b66\u590d\u4e60\u8d44\u6599\u6574\u7406<\/strong><\/p>\n

(1)\u76f4\u7ebf\u7684\u503e\u659c\u89d2<\/p>\n

\u5b9a\u4e49\uff1ax\u8f74\u6b63\u5411\u4e0e\u76f4\u7ebf\u5411\u4e0a\u65b9\u5411\u4e4b\u95f4\u6240\u6210\u7684\u89d2\u53eb\u76f4\u7ebf\u7684\u503e\u659c\u89d2.\u7279\u522b\u5730,\u5f53\u76f4\u7ebf\u4e0ex\u8f74\u5e73\u884c\u6216\u91cd\u5408\u65f6,\u6211\u4eec\u89c4\u5b9a\u5b83\u7684\u503e\u659c\u89d2\u4e3a0\u5ea6.\u56e0\u6b64,\u503e\u659c\u89d2\u7684\u53d6\u503c\u8303\u56f4\u662f0\u00b0\u2264\u03b1<180\u00b0<\/p>\n

(2)\u76f4\u7ebf\u7684\u659c\u7387<\/p>\n

\u2460\u5b9a\u4e49\uff1a\u503e\u659c\u89d2\u4e0d\u662f90\u00b0\u7684\u76f4\u7ebf,\u5b83\u7684\u503e\u659c\u89d2\u7684\u6b63\u5207\u53eb\u505a\u8fd9\u6761\u76f4\u7ebf\u7684\u659c\u7387.\u76f4\u7ebf\u7684\u659c\u7387\u5e38\u7528k\u8868\u793a.\u5373.\u659c\u7387\u53cd\u6620\u76f4\u7ebf\u4e0e\u8f74\u7684\u503e\u659c\u7a0b\u5ea6.<\/p>\n

\u5f53\u65f6,;\u5f53\u65f6,;\u5f53\u65f6,\u4e0d\u5b58\u5728.<\/p>\n

\u2461\u8fc7\u4e24\u70b9\u7684\u76f4\u7ebf\u7684\u659c\u7387\u516c\u5f0f\uff1a<\/p>\n

\u6ce8\u610f\u4e0b\u9762\u56db\u70b9\uff1a(1)\u5f53\u65f6,\u516c\u5f0f\u53f3\u8fb9\u65e0\u610f\u4e49,\u76f4\u7ebf\u7684\u659c\u7387\u4e0d\u5b58\u5728,\u503e\u659c\u89d2\u4e3a90\u00b0;<\/p>\n

(2)k\u4e0eP1\u3001P2\u7684\u987a\u5e8f\u65e0\u5173;(3)\u4ee5\u540e\u6c42\u659c\u7387\u53ef\u4e0d\u901a\u8fc7\u503e\u659c\u89d2\u800c\u7531\u76f4\u7ebf\u4e0a\u4e24\u70b9\u7684\u5750\u6807\u76f4\u63a5\u6c42\u5f97;<\/p>\n

(4)\u6c42\u76f4\u7ebf\u7684\u503e\u659c\u89d2\u53ef\u7531\u76f4\u7ebf\u4e0a\u4e24\u70b9\u7684\u5750\u6807\u5148\u6c42\u659c\u7387\u5f97\u5230.<\/p>\n

(3)\u76f4\u7ebf\u65b9\u7a0b<\/p>\n

\u2460\u70b9\u659c\u5f0f\uff1a\u76f4\u7ebf\u659c\u7387k,\u4e14\u8fc7\u70b9<\/p>\n

\u6ce8\u610f\uff1a\u5f53\u76f4\u7ebf\u7684\u659c\u7387\u4e3a0\u00b0\u65f6,k=0,\u76f4\u7ebf\u7684\u65b9\u7a0b\u662fy=y1.<\/p>\n

\u5f53\u76f4\u7ebf\u7684\u659c\u7387\u4e3a90\u00b0\u65f6,\u76f4\u7ebf\u7684\u659c\u7387\u4e0d\u5b58\u5728,\u5b83\u7684\u65b9\u7a0b\u4e0d\u80fd\u7528\u70b9\u659c\u5f0f\u8868\u793a.\u4f46\u56e0l\u4e0a\u6bcf\u4e00\u70b9\u7684\u6a2a\u5750\u6807\u90fd\u7b49\u4e8ex1,\u6240\u4ee5\u5b83\u7684\u65b9\u7a0b\u662fx=x1.<\/p>\n

\u2461\u659c\u622a\u5f0f\uff1a,\u76f4\u7ebf\u659c\u7387\u4e3ak,\u76f4\u7ebf\u5728y\u8f74\u4e0a\u7684\u622a\u8ddd\u4e3ab<\/p>\n

\u2462\u4e24\u70b9\u5f0f\uff1a()\u76f4\u7ebf\u4e24\u70b9,<\/p>\n

\u2463\u622a\u77e9\u5f0f\uff1a<\/p>\n

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\u2464\u4e00\u822c\u5f0f\uff1a(A,B\u4e0d\u5168\u4e3a0)<\/p>\n

\u6ce8\u610f\uff1a\u5404\u5f0f\u7684\u9002\u7528\u8303\u56f4\u7279\u6b8a\u7684\u65b9\u7a0b\u5982\uff1a<\/p>\n

\u5e73\u884c\u4e8ex\u8f74\u7684\u76f4\u7ebf\uff1a(b\u4e3a\u5e38\u6570);\u5e73\u884c\u4e8ey\u8f74\u7684\u76f4\u7ebf\uff1a(a\u4e3a\u5e38\u6570);<\/p>\n

(5)\u76f4\u7ebf\u7cfb\u65b9\u7a0b\uff1a\u5373\u5177\u6709\u67d0\u4e00\u5171\u540c\u6027\u8d28\u7684\u76f4\u7ebf<\/p>\n

(\u4e00)\u5e73\u884c\u76f4\u7ebf\u7cfb<\/p>\n

\u5e73\u884c\u4e8e\u5df2\u77e5\u76f4\u7ebf(\u662f\u4e0d\u5168\u4e3a0\u7684\u5e38\u6570)\u7684\u76f4\u7ebf\u7cfb\uff1a(C\u4e3a\u5e38\u6570)<\/p>\n

(\u4e8c)\u5782\u76f4\u76f4\u7ebf\u7cfb<\/p>\n

\u5782\u76f4\u4e8e\u5df2\u77e5\u76f4\u7ebf(\u662f\u4e0d\u5168\u4e3a0\u7684\u5e38\u6570)\u7684\u76f4\u7ebf\u7cfb\uff1a(C\u4e3a\u5e38\u6570)<\/p>\n

(\u4e09)\u8fc7\u5b9a\u70b9\u7684\u76f4\u7ebf\u7cfb<\/p>\n

(\u2170)\u659c\u7387\u4e3ak\u7684\u76f4\u7ebf\u7cfb\uff1a,\u76f4\u7ebf\u8fc7\u5b9a\u70b9;<\/p>\n

(\u2171)\u8fc7\u4e24\u6761\u76f4\u7ebf,\u7684\u4ea4\u70b9\u7684\u76f4\u7ebf\u7cfb\u65b9\u7a0b\u4e3a<\/p>\n

(\u4e3a\u53c2\u6570),\u5176\u4e2d\u76f4\u7ebf\u4e0d\u5728\u76f4\u7ebf\u7cfb\u4e2d.<\/p>\n

(6)\u4e24\u76f4\u7ebf\u5e73\u884c\u4e0e\u5782\u76f4<\/p>\n

\u6ce8\u610f\uff1a\u5229\u7528\u659c\u7387\u5224\u65ad\u76f4\u7ebf\u7684\u5e73\u884c\u4e0e\u5782\u76f4\u65f6,\u8981\u6ce8\u610f\u659c\u7387\u7684\u5b58\u5728\u4e0e\u5426.<\/p>\n

\u9ad8\u4e2d\u6570\u5b66\u590d\u4e60\u8d44\u6599<\/strong><\/p>\n

(1) \u5e38\u89c4\u7684\u7ebf\u6027\u89c4\u5212\u95ee\u9898\uff0c\u5373\u6c42\u5728\u7ebf\u6027\u7ea6\u675f\u6761\u4ef6\u4e0b\u7684\u6700\u503c\u95ee\u9898;<\/p>\n

(2) \u4e0e\u51fd\u6570\u3001\u5e73\u9762\u5411\u91cf\u7b49\u77e5\u8bc6\u7ed3\u5408\u7684\u6700\u503c\u7c7b\u95ee\u9898;<\/p>\n

(3) \u6c42\u5728\u975e\u7ebf\u6027\u7ea6\u675f\u6761\u4ef6\u4e0b\u7684\u6700\u503c\u95ee\u9898;<\/p>\n

(4) \u8003\u67e5\u7ebf\u6027\u89c4\u5212\u95ee\u9898\u5728\u89e3\u51b3\u5b9e\u9645\u751f\u6d3b\u3001\u751f\u4ea7\u5b9e\u9645\u4e2d\u7684\u5e94\u7528.\u800c\u5176\u4e2d\u7684\u7b2c(2)(3)(4)\u70b9\u5f80\u5f80\u662f\u547d\u9898\u7684\u521b\u65b0\u70b9\u3002<\/p>\n

\u3010\u4f8b1\u3011 \u8bbe\u51fd\u6570f(\u03b8)=?3?sin?\u03b8+??cos?\u03b8\uff0c\u5176\u4e2d\uff0c\u89d2\u03b8\u7684\u9876\u70b9\u4e0e\u5750\u6807\u539f\u70b9\u91cd\u5408\uff0c\u59cb\u8fb9\u4e0ex\u8f74\u975e\u8d1f\u534a\u8f74\u91cd\u5408\uff0c\u7ec8\u8fb9\u7ecf\u8fc7\u70b9?p(x,y)?\uff0c\u4e140\u2264\u03b8\u2264?\u03c0?\u3002<\/p>\n

(1) \u82e5\u70b9p\u7684\u5750\u6807\u4e3a12,32\uff0c\u6c42f(\u03b8)\u7684\u503c;<\/p>\n

(2) \u82e5\u70b9p(x,y)\u4e3a\u5e73\u9762\u533a\u57df\u03c9\uff1ax+y\u22651,x\u22641,y\u22641\u3002 \u4e0a\u7684\u4e00\u4e2a\u52a8\u70b9\uff0c\u8bd5\u786e\u5b9a\u89d2\u03b8\u7684\u53d6\u503c\u8303\u56f4\uff0c\u5e76\u6c42\u51fd\u6570f(\u03b8)\u7684\u6700\u5c0f\u503c\u548c\u6700\u5927\u503c\u3002<\/p>\n

\u5206\u6790 \u7b2c(1)\u95ee\u53ea\u9700\u8981\u8fd0\u7528\u4e09\u89d2\u51fd\u6570\u7684\u5b9a\u4e49\u5373\u53ef;\u7b2c(2)\u95ee\u4e2d\u53ea\u8981\u5148\u753b\u51fa\u5e73\u9762\u533a\u57df\u03c9\uff0c\u518d\u6839\u636e\u62bd\u753b\u51fa\u7684\u5e73\u9762\u533a\u57df\u786e\u5b9a\u89d2\u03b8\u7684\u53d6\u503c\u8303\u56f4\uff0c\u8fdb\u800c\u8f6c\u5316\u4e3a\u6c42f(\u03b8)=a?sin?\u03b8+b?cos?\u03b8\u578b\u51fd\u6570\u7684\u6700\u503c\u3002<\/p>\n

\u89e3 (1) \u7531\u70b9p\u7684\u5750\u6807\u548c\u4e09\u89d2\u51fd\u6570\u7684\u5b9a\u4e49\u53ef\u5f97?sin?\u03b8=32\uff0c?cos?\u03b8=12\u3002<\/p>\n

\u4e8e\u662ff(\u03b8)=3?sin?\u03b8+??cos?\u03b8=?3\u00d732+12=2\u3002<\/p>\n

(2) \u4f5c\u51fa\u5e73\u9762\u533a\u57df\u03c9 (\u5373\u4e09\u89d2\u5f62\u533a\u57dfabc)\u5982\u56fe\u6240\u793a\uff0c\u5176\u4e2da(1,0)\uff0cb(1,1)\uff0c?c(0,1)?.\u4e8e\u662f0\u2264\u03b8\u2264?\u03c0?2,<\/p>\n

\u53c8f(\u03b8)=3?sin?\u03b8+?cos?\u03b8=2?sin?\u03b8+?\u03c0?6\uff0c<\/p>\n

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\n

<\/em>\u9ad8\u4e2d\u6570\u5b66\u590d\u4e60\u8d44\u6599\u603b\u7ed3\u76f8\u5173\u6587\u7ae0\uff1a<\/strong><\/p>\n

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\u2605 2021\u9ad8\u4e2d\u6570\u5b66\u7684\u6700\u8be6\u7ec6\u91cd\u70b9\u77e5\u8bc6\u70b9\u5168\u603b\u7ed3<\/p>\n

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\u2605 2021\u9ad8\u4e2d\u6570\u5b66\u57fa\u672c\u77e5\u8bc6\u70b9\u51b2\u523a\u603b\u7ed3<\/p>\n

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