{"id":45830,"date":"2013-10-18T14:18:29","date_gmt":"2013-10-18T06:18:29","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=45830"},"modified":"2021-10-06T16:20:02","modified_gmt":"2021-10-06T08:20:02","slug":"%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b8%e5%80%bc%e8%a1%a8","status":"publish","type":"post","link":"http:\/\/localhost\/%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b8%e5%80%bc%e8%a1%a8\/","title":{"rendered":"\u4e09\u89d2\u51fd\u6578\u503c\u8868"},"content":{"rendered":"

\u4e09\u89d2\u51fd\u6578\u503c\u8868<\/strong><\/span>
\n \u570b\u7acb\u862d\u967d\u5973\u4e2d\u6578\u5b78\u79d1\u9673\u654f\u6667\u8001\u5e2b<\/strong><\/span><\/p>\n

\u4e09\u89d2\u51fd\u6578\u503c\u8868\uff1a\u73fe\u884c\u7684\u4e09\u89d2\u51fd\u6578\u503c\u8868\uff0c\u662f\u5c07\u4e09\u89d2\u51fd\u6578\u7684\u8fd1\u4f3c\u503c\u7b97\u51fa\u4e26\u88fd\u6210\u8868\u683c\uff0c\u8868\u5f9e $$0^\\circ$$ \u5230 $$90^\\circ$$ \u9593(\u4ee5 $$10’$$ \u70ba\u55ae\u4f4d\uff0c$$1^\\circ=60’$$)\u7684\u5404\u7a2e\u4e09\u89d2\u51fd\u6578\u503c\uff0c\u8d85\u904e $$90^\\circ$$ \u6216\u5c0f\u65bc $$0^\\circ$$ \u7684\u89d2\uff0c\u518d\u5229\u7528\u5ee3\u7fa9\u89d2\u7684\u6027\u8cea\u8f49\u63db\u3002\u8868\u4e2d\u6700\u5de6\u4e00\u884c\u7531\u4e0a\u800c\u4e0b\u5448\u73fe\u7684\u89d2\u5ea6\u662f\u905e\u589e\u60c5\u5f62\uff0c\u5c0d\u61c9\u6700\u4e0a\u4e00\u5217\u7531\u5de6\u800c\u53f3\u6709 $$\\sin$$\u3001<\/strong>$$\\cos$$\u3001$$\\tan$$\u3001$$\\cot$$\u3001$$\\sec$$\u3001$$\\csc$$ \u5404\u500b\u51fd\u6578\u7b26\u865f\uff1b\u8868\u4e2d\u6700\u53f3\u4e00\u884c\u7531\u4e0b\u800c\u4e0a\u5448\u73fe\u7684\u89d2\u5ea6\u662f\u905e\u589e\u60c5\u5f62\uff0c\u5c0d\u61c9\u6700\u4e0b\u4e00\u5217\u7531\u5de6\u800c\u53f3\u5370\u6709 $$\\cos$$\u3001$$\\sin$$\u3001$$\\cot$$\u3001$$\\tan$$\u3001$$\\csc$$\u00a0\u548c $$\\sec$$ \u5404\u500b\u51fd\u6578\u7b26\u865f\uff0c\u56e0\u6b64\uff0c\u67e5\u8868\u7684\u7c21\u6613\u53e3\u8a23\u70ba\u300c\u5de6\u4e0a\u53f3\u4e0b\u300d\uff0c\u4e0b\u5716\u4e00\u70ba\u4e09\u89d2\u51fd\u6578\u503c\u8868\u7684\u90e8\u5206\u8868\u683c\u3002<\/p>\n

\"45830_p1\"<\/a>

\u5716\u4e00$$~~~$$\u4e09\u89d2\u51fd\u6578\u503c\u8868\u7684\u90e8\u5206\u8868\u683c<\/p><\/div>\n

\u6839\u64da\u4e0a\u8868\u5f97\u77e5\uff1a<\/p>\n

$$\\sin 12^\\circ 50′ = 0.2221$$\uff0c$$\\cos 12^\\circ 50′ = 0.9750$$\uff0c$$\\tan 12^\\circ 50′ = 0.2278$$\uff0c$$\\cot 12^\\circ 50′ = 4.3897$$\uff0c$$\\sec 12^\\circ 50′ = 1.0256$$\uff0c$$\\csc 12^\\circ 50′ = 4.5022$$\uff1b<\/p>\n

\u5229\u7528\u9918\u89d2\u95dc\u4fc2<\/p>\n

$$\\sin ({90^\\circ}-\\theta ) = \\cos \\theta$$\uff0c$$\\cos({90^\\circ}-\\theta ) = \\sin \\theta$$\uff0c$$\\tan ({90^\\circ}-\\theta ) = \\cot \\theta$$\uff0c$$\\cot ({90^\\circ}-\\theta ) = \\tan \\theta$$\uff0c$$\\sec ({90^\\circ}-\\theta ) = \\csc \\theta$$\uff0c$$\\csc ({90^\\circ}-\\theta ) = \\sec \\theta$$
\n\u53ca $$90^\\circ-12^\\circ 50’=77^\\circ 10’$$\uff0c<\/p>\n

\u53ef\u67e5\u51fa<\/p>\n

$$\\sin 77^\\circ 10’=0.9750$$\uff0c$$\\cos 77^\\circ 10’=0.2221$$\uff0c$$\\tan 77^\\circ 10’=4.3897$$\uff0c$$\\cot 77^\\circ 10’=0.2278$$\uff0c$$\\sec{77^\\circ}10’=4.5022$$\uff0c$$\\csc 77^\\circ 10’=1.0256$$\u3002<\/p>\n

\u56e0\u6b64\uff0c\u5728\u67e5\u4e09\u89d2\u51fd\u6578\u6642\u9700\u6ce8\u610f\u300c\u5de6\u4e0a\u53f3\u4e0b\u300d\u9019\u500b\u7279\u6b8a\u7d50\u69cb\u3002<\/p>\n

\u81f3\u65bc\u89d2\u5ea6\u975e $$10’$$ \u7684\u500d\u6578\u6642\uff0c\u53ef\u5229\u7528\u5167\u63d2\u6cd5\uff0c\u65b9\u6cd5\u662f\u5148\u627e\u76f8\u9130\u5169\u89d2\u7684\u4e09\u89d2\u51fd\u6578\u503c\uff0c\u7136\u5f8c\u5229\u7528\u7dda\u6027\u7684\u6bd4\u4f8b\u95dc\u4fc2\u6c42\u77e5\u5f97\u8fd1\u4f3c\u503c\uff0c<\/p>\n

\u4f8b\u5982\uff1a\u6c42 $$\\sin 12^\\circ 53’=?$$<\/p>\n

\u53ef\u5148\u67e5\u8868\u77e5 $$\\sin 12^\\circ 50’=0.2221$$\uff0c$$\\sin 13^\\circ 00’=0.2225$$<\/p>\n

\u518d\u5229\u7528\u5167\u63d2\u6cd5\uff0c\u5f97 $$\\displaystyle\\frac{{\\sin {{12}^\\circ}53′ – 0.2221}}{{0.2225 – 0.2221}} = \\frac{{{{12}^\\circ}53′ – {{12}^\\circ}50′}}{{{{13}^\\circ}00′ – {{12}^\\circ}50′}} = \\frac{3}{{10}}$$\uff0c<\/p>\n

\u79fb\u9805\u53ef\u5f97 $$\\sin 12^\\circ 53′-0.2221=0.00012$$\uff0c\u5247 $$\\sin 12^\\circ 53’=0.22222\\approx 0.2222$$\u3002<\/p>\n

\u9047\u5230\u5ee3\u7fa9\u89d2\u7684\u8655\u7406\u65b9\u5f0f\uff0c\u5247\u5148\u8f49\u63db\u6210\u92b3\u89d2\u4e09\u89d2\u51fd\u6578\uff0c\u518d\u5229\u7528\u67e5\u8868\uff0c\u91cd\u8907\u4e0a\u8ff0\u52d5\u4f5c\uff0c\u5373\u53ef\u5b8c\u6210\u3002<\/p>\n

\u53e4\u4ee3\u4e2d\u570b\u7684\u300a\u4e5d\u6267\u66c6\u300b\u4e2d\u6709\u7403\u9762\u4e09\u89d2\u63a8\u7b97\u6708\u98df\u6642\u6708\u7403\u96e2\u9ec3\u9053\u7684\u5ea6\u6578\uff0c\u5176\u4e2d\u6709\u300c\u63a8\u6708\u9593\u91cf\u547d\u300d\u8a18\u8f09\uff0c\u865f\u70ba\u4e2d\u570b\u6700\u65e9\u7684\u4e09\u89d2(\u6b63\u5f26)\u51fd\u6578\u503c\u8868\uff0c\u82f1\u570b\u79d1\u5b78\u53f2\u5bb6\u674e\u7d04\u745f\u535a\u58eb(Joseph Needham, 1900-1995)\u7a31\u4e4b\u70ba\u300c\u4e09\u89d2\u5b78\u7684\u6700\u65e9\u5f62\u614b\u300d\uff0c\u539f\u5f15\u6587\u5982\u4e0b\uff1a<\/p>\n

\u63a8\u6708\u9593\u91cf\u547d\uff1a\u6bb5\u6cd5\uff0c\u51e1\u4e00\u6bb5\u7ba1\u4e09\u5ea6\u56db\u5341\u4e94\u5206\uff0c\u6bcf\u516b\u6bb5\u7ba1\u4e00\u76f8\uff0c\u7e3d\u6709\u4e8c\u5341\u56db\u6bb5\uff0c\u7528\u7ba1\u4e09\u76f8\uff0c\u5176\u6bb5\u4e0b\u4f8b\u6ce8\u8005\uff0c<\/strong>\u662f\u7a4d\u6bb5\u5e76\u6210\u4e4b\u6578\u3002\u7b2c\u4e00\u6bb5\uff0c\u4e8c\u767e\u4e8c\u5341\u4e94\u2026\u2026<\/strong><\/p>\n

\u56e0\u70ba\u5728\u300a\u4e5d\u6267\u66c6\u300b\u4e2d\u4e00\u5713\u5468\u70ba $$360$$ \u5ea6\uff0c\u6bcf\u5ea6\u518d\u7d30\u5206 $$60$$ \u5206\uff0c\u5247 $$360^\\circ=21600’$$\uff0c\u4ee5 $$2\\pi$$ \u9664\u4e4b\uff0c\u82e5 $$\\pi$$ \u53d6 $$3.14$$\uff0c\u5546\u6578\u70ba $$3439.4904’$$\uff1b\u82e5 $$\\pi$$ \u53d6 $$3.1416$$\uff0c\u5546\u6578\u70ba $$3437.7387’$$\uff0c\u56e0\u70ba\u300c\u7b2c\u4e8c\u5341\u56db\u6bb5\uff0c\u4e03\uff0c\u5e76\u4e09\u5343\u56db\u767e\u4e09\u5341\u516b\u3002\u300d\u53ef\u898b\u300a\u4e5d\u6267\u66c6\u300b\u4e2d\u5713\u5468\u7387 $$\\pi$$ \u7684\u8fd1\u4f3c\u503c\u53d6 $$3.1416$$\uff0c\u4e0a\u5f15\u6587\u4e2d\u7684\u4e8c\u5341\u56db\u6bb5\uff0c\u5373\u5c07 $$90^\\circ\/24=3.75^\\circ=3^\\circ 45’$$\uff0c\u7b2c\u4e00\u53e5\u8a71\u300c\u7b2c\u4e00\u6bb5\uff0c\u4e8c\u767e\u4e8c\u5341\u4e94\u300d\u5373 $$\\sin 3^\\circ 45’=\\frac{225}{3438}=0.06544$$\u3002<\/p>\n\n\n\n\n
\u6bb5\u6578<\/td>\n\u89d2\u5ea6$$\\theta$$<\/td>\n3438$$\\sin\\theta$$<\/td>\n$$\\sin\\theta^1$$<\/td>\n\u6b63\u78ba\u6b63\u5f26\u503c<\/td>\n\u8aa4\u5dee\u6578<\/td>\n<\/tr>\n
1<\/td>\n$$3^\\circ45’$$<\/td>\n225<\/td>\n0.0654<\/td>\n0.0655<\/td>\n0.0001<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

1 \u00a0<\/sup>\u6b64\u8655\u7684\u6b63\u5f26\u51fd\u6578\u503c\u53d6\u81f3\u5c0f\u6578\u9ede\u5f8c\u7b2c\u56db\u4f4d,\u5c0f\u6578\u9ede\u5f8c\u7b2c\u4e94\u4f4d\u56db\u6368\u4e94\u5165\u3002<\/p>\n

\n

\u9664\u4e86\u4e2d\u570b\u53e4\u7b97\u66f8\u300a\u4e5d\u6267\u66c6\u300b\u7684\u8a18\u8f09\u4e4b\u5916,\u6e05\u4ee3\u4e5f\u6709\u66c6\u66f8\u6587\u672c\u5448\u73fe\u4e09\u89d2\u51fd\u6578\u503c\u8868, \u4e0b\u5716\u4e8c\u5c31\u662f\u4e00\u4efd\u8499\u53e4\u7684\u6578\u5b78\u6587\u672c,\u6240\u5448\u73fe\u7684\u4e09\u89d2\u51fd\u6578\u503c\u7684\u89d2\u5ea6\u4ecb\u65bc $$44^\\circ 30’$$ \u5230$$45^\\circ 00’$$, \u6839\u64da\u6578\u5b78\u53f2\u5bb6\u56b4\u6566\u6770\u7684\u7814\u7a76, \u9019\u4efd\u6587\u672c\u53ef\u56de\u6eaf\u81f3 1712 \u5e74\u7684\u6e6f\u82e5\u671b\u300a\u5d07\u798e\u66c6\u66f8\u300b\u6539\u7248\u672c\u30022<\/sup><\/a><\/p>\n

\"45830_p2\"<\/a>

\u5716\u4e8c$$~~~$$\u300a\u5d07\u798e\u66c6\u66f8\u300b\u4e2d\u7684\u4e09\u89d2\u51fd\u6578\u503c\u8868<\/p><\/div>\n

\u81f3\u65bc\u5e0c\u81d8\u5929\u6587\u5b78\u5bb6\u6258\u52d2\u5bc6\u662f\u5982\u4f55\u7de8\u5236\u5f26\u8868\uff1f\u8a73\u60c5\u53ef\u4ee5\u53c3\u95b1\u8521\u8070\u660e\uff0c\u3008\u661f\u7a7a\u71e6\u721b\u7684\u6578\u5b78(\u0399)-\u6258\u52d2\u5bc6\u5982\u4f55\u7de8\u5236\u5f26\u8868\uff1f\u3009\uff0c\u300a\u6578\u5b78\u50b3\u64ad\u300b\uff0c23\u53772\u671f(\u6c1188\u5e746\u6708)\uff0c\u980157-67\uff0c\u6587\u4e2d\u5c0d\u65bc\u5f26\u8868\u7684\u5c0e\u51fa\u904e\u7a0b\uff0c\u6709\u5b8c\u6574\u7684\u5448\u73fe\u3002<\/p>\n

\n

\u53c3\u8003\u8cc7\u6599<\/span><\/strong><\/p>\n

    \n
  1. \u6bdb\u723e(Eli Maor)\uff0c\u80e1\u5b88\u4ec1\u8b6f\uff0c\u300a\u6bdb\u8d77\u4f86\u8aaa\u4e09\u89d2\u300b\uff0c\u53f0\u5317\uff1a\u5929\u4e0b\u9060\u898b\u51fa\u7248\u793e\uff0c2000\u3002<\/span><\/li>\n
  2. Jean-Claude Martzloff, A History of Chinese Mathematics<\/i>, Heidelberg : Springer-Verlag, 1997.<\/span><\/li>\n
  3. \u8521\u8070\u660e\uff0c\u3008\u661f\u7a7a\u71e6\u721b\u7684\u6578\u5b78(\u0399)-\u6258\u52d2\u5bc6\u5982\u4f55\u7de8\u5236\u5f26\u8868\uff1f\u3009<\/span><\/li>\n<\/ol>\n<\/div>\n
    \n

    <\/a>2 \u00a0<\/sup>\u6b64\u8655\u7684\u6b63\u5f26\u51fd\u6578\u503c\u53d6\u81f3\u5c0f\u6578\u9ede\u5f8c\u7b2c\u56db\u4f4d,\u5c0f\u6578\u9ede\u5f8c\u7b2c\u4e94\u4f4d\u56db\u6368\u4e94\u5165\u3002<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u4e09\u89d2\u51fd\u6578\u503c\u8868 \u570b\u7acb\u862d\u967d\u5973\u4e2d\u6578\u5b78\u79d1\u9673\u654f\u6667\u8001\u5e2b \u4e09\u89d2\u51fd\u6578\u503c\u8868\uff1a\u73fe\u884c\u7684\u4e09\u89d2\u51fd\u6578\u503c\u8868\uff0c\u662f\u5c07\u4e09\u89d2\u51fd\u6578\u7684\u8fd1\u4f3c\u503c\u7b97\u51fa\u4e26\u88fd\u6210\u8868…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[222,111],"tags":[822,1586],"class_list":["post-45830","post","type-post","status-publish","format-standard","hentry","category-math03-03","category-mathematics00","tag-822","tag-1586","loop-entry","cat-222","cat-111","no-thumbnail"],"views":21540,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/45830","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=45830"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/45830\/revisions"}],"predecessor-version":[{"id":87405,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/45830\/revisions\/87405"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=45830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=45830"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=45830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}