高二职高数学 高二数学。
\u804c\u9ad8\u9ad8\u4e8c\u6570\u5b66\u5168\u516c\u5f0f\u4e09\u89d2\u5b66
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sin\u03b8\uff1db/c\u3000\u3000cos\u03b8\uff1da/c\u3000\u3000tan\u03b8\uff1db/a
csc\u03b8\uff1dc/b\u3000\u3000sec\u03b8\uff1dc/a\u3000\u3000cot\u03b8\uff1da/b
\u3000\u3000
\u82e5\u5706\u7684\u534a\u5f84\u662f1\uff0c\u5219\u5176\u6b63\u5f26\u4e0e\u4f59\u5f26\u5206\u522b\u4e3a\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u9ad8\u4e0e\u5e95\u3002
a\uff1dcos\u03b8\u3000\u3000\u3000\u3000b\uff1dsin\u03b8
\u4f9d\u7167\u52fe\u80a1\u5b9a\u7406,\u6211\u4eec\u77e5\u9053a2\uff0bb2\uff1dc2\u3002\u56e0\u6b64\u5bf9\u4e8e\u5706\u4e0a\u7684\u4efb\u4f55\u89d2\u5ea6\u03b8\uff0c\u6211\u4eec\u90fd\u53ef\u5f97\u51fa\u4e0b\u5217\u7684\u5168\u7b49\u5f0f\uff1a
cos2\u03b8\uff0bsin2\u03b8\uff1d1
\u4e09\u89d2\u6052\u7b49\u5f0f
\u3000
\u6839\u636e\u524d\u51e0\u9875\u6240\u8ff0\u7684\u5b9a\u4e49\uff0c\u53ef\u5f97\u5230\u4e0b\u5217\u6052\u7b49\u5f0f\uff08identity\uff09\uff1a
tan\u03b8\uff1dsin\u03b8/cos\u03b8\uff0ccot\u03b8\uff1dcos\u03b8/sin\u03b8
sec\u03b8\uff1d1/cos\u03b8\uff0ccsc\u03b8\uff1d1/sin\u03b8
\u3000\u3000
\u5206\u522b\u7528cos 2\u03b8\u4e0esin 2\u03b8\u6765\u9664cos 2\u03b8\uff0bsin 2\u03b8\uff1d1\uff0c\u53ef\u5f97\uff1a
sec 2\u03b8\u2013tan 2\u03b8\uff1d1\u3000\u3000\u53ca\u3000\u3000csc 2\u03b8\u2013cot 2\u03b8\uff1d1
\u5bf9\u4e8e\u8d1f\u89d2\u5ea6\uff0c\u516d\u4e2a\u4e09\u89d2\u51fd\u6570\u5206\u522b\u4e3a\uff1a
sin(\u2013\u03b8)\uff1d \u2013sin\u03b8 \u3000csc(\u2013\u03b8)\uff1d \u2013csc\u03b8
cos(\u2013\u03b8)\uff1d cos\u03b8\u3000\u3000sec(\u2013\u03b8)\uff1d sec\u03b8
tan(\u2013\u03b8)\uff1d \u2013tan\u03b8\u3000 cot(\u2013\u03b8)\uff1d \u2013cot\u03b8
\u3000\u3000
\u5f53\u4e24\u89d2\u5ea6\u76f8\u52a0\u65f6\uff0c\u8fd0\u7528\u548c\u89d2\u516c\u5f0f\uff1a
sin(\u03b1\uff0b\u03b2)\uff1d sin\u03b1cos\u03b2\uff0bcos\u03b1sin\u03b2
cos(\u03b1\uff0b\u03b2)\uff1d cos\u03b1cos\u03b2\u2013sin\u03b1sin\u03b2
tan(\u03b1\uff0b\u03b2)\uff1d tan\u03b1\uff0btan\u03b2\uff0f1\u2013tan\u03b1tan\u03b2
\u82e5\u9047\u5230\u4e24\u500d\u89d2\u6216\u4e09\u500d\u89d2\uff0c\u8fd0\u7528\u500d\u89d2\u516c\u5f0f\uff1a
sin2\u03b1\uff1d 2sin\u03b1cos\u03b1\u3000 sin3\u03b1\uff1d 3sin\u03b1cos2\u03b1\u2013sin3\u03b1
cos2\u03b1\uff1d cos 2\u03b1\u2013sin 2\u03b1\u3000cos3\u03b1\uff1d cos 3\u03b1\u20133sin 2\u03b1cos\u03b1
tan 2\u03b1\uff1d 2tan\u03b1\uff0f1\u2013tan 2\u03b1
tan3\u03b1\uff1d 3tan\u03b1\u2013tan 3\u03b1\uff0f1\u20133tan 2\u03b1
\u4e8c\u7ef4\u56fe\u5f62
\u4e0b\u9762\u662f\u4e00\u4e9b\u4e8c\u7ef4\u56fe\u5f62\u7684\u5468\u957f\u4e0e\u9762\u79ef\u516c\u5f0f\u3002
\u5706\uff1a
\u534a\u5f84\uff1d r\u3000\u3000\u3000\u3000\u76f4\u5f84d\uff1d2r
\u5706\u5468\u957f\uff1d 2\u03c0r \uff1d\u03c0d
\u9762\u79ef\uff1d\u03c0r2\u3000 (\u03c0\uff1d3.1415926\u2026\u2026.)
\u692d\u5706\uff1a
\u9762\u79ef\uff1d\u03c0ab
a\u4e0eb\u5206\u522b\u4ee3\u8868\u77ed\u8f74\u4e0e\u957f\u8f74\u7684\u4e00\u534a\u3002
\u77e9\u5f62\uff1a
\u9762\u79ef\uff1d ab
\u5468\u957f\uff1d 2a\uff0b2b
\u5e73\u884c\u56db\u8fb9\u5f62\uff08parallelogram\uff09\uff1a
\u9762\u79ef\uff1d bh \uff1d ab sin\u03b1
\u5468\u957f\uff1d 2a\uff0b2b
\u68af\u5f62\uff1a
\u9762\u79ef\uff1d 1/2h (a\uff0bb)
\u5468\u957f\uff1d a\uff0bb\uff0bh (sec\u03b1\uff0bsec\u03b2)
\u6b63n\u8fb9\u5f62\uff1a
\u9762\u79ef\uff1d 1/2nb2 cot (180\u00b0/n)
\u5468\u957f\uff1d nb
\u56db\u8fb9\u5f62\uff08i\uff09\uff1a
\u9762\u79ef\uff1d 1/2ab sin\u03b1
\u56db\u8fb9\u5f62\uff08ii\uff09\uff1a
\u9762\u79ef\uff1d 1/2 (h1\uff0bh2) b\uff0bah1\uff0bch2
\u4e09\u7ef4\u56fe\u5f62
\u4ee5\u4e0b\u662f\u4e09\u7ef4\u7acb\u4f53\u7684\u4f53\u79ef\u4e0e\u8868\u9762\u79ef\uff08\u5305\u542b\u5e95\u90e8\uff09\u516c\u5f0f\u3002
\u7403\u4f53\uff1a
\u4f53\u79ef\uff1d 4/3\u03c0r3
\u8868\u9762\u79ef\uff1d 4\u03c0r2
\u65b9\u4f53\uff1a
\u4f53\u79ef\uff1d abc
\u8868\u9762\u79ef\uff1d 2(ab\uff0bac\uff0bbc)
\u5706\u67f1\u4f53\uff1a
\u4f53\u79ef\uff1d \u03c0r2h
\u8868\u9762\u79ef\uff1d 2\u03c0rh\uff0b2\u03c0r2
\u5706\u9525\u4f53\uff1a
\u4f53\u79ef\uff1d 1/3\u03c0r2h
\u8868\u9762\u79ef\uff1d\u03c0r\u221ar2\uff0bh2 \uff0b\u03c0r2
\u4e09\u89d2\u9525\u4f53\uff1a
\u82e5\u5e95\u9762\u79ef\u4e3aA\uff0c
\u4f53\u79ef\uff1d 1/3Ah
\u5e73\u622a\u5934\u4f53\uff08frustum\uff09\uff1a
\u4f53\u79ef\uff1d 1/3\u03c0h (a2\uff0bab\uff0bb2)
\u8868\u9762\u79ef\uff1d\u03c0(a\uff0bb)c\uff0b\u03c0a2\uff0b\u03c0b2
\u692d\u7403\uff1a
\u4f53\u79ef\uff1d 4/3\u03c0abc
\u73af\u9762\uff08torus\uff09\uff1a
\u4f53\u79ef\uff1d 1/4\u03c02 (a\uff0bb) (b\u2013a) 2
\u8868\u9762\u79ef\uff1d\u03c02 (b2\u2013a2)
\u5982\u56fe
如图所示
绛旓細鑱岄珮鏁板鍜屾櫘閫氶珮涓暟瀛﹀尯鍒亴楂樻暟瀛﹀拰鏅氶珮涓殑鍖哄埆涓嶅ぇ锛岀煡璇嗙偣鏄ぇ鑷寸浉鍚岀殑锛屽氨杩炴彁绾查兘寰堢浉浼硷紝浣嗘槸鑱岄珮鏁板鐨勭煡璇嗛噺骞舵病鏈夐偅涔堝锛屾瘮濡傚鏁颁笌瀹氱Н鍒嗛兘娌℃湁瑕佹眰瀛︿範锛岃屾櫘閫氶珮涓偗瀹氳瀛︿範杩欎簺銆傝亴楂樻暟瀛︾煡璇嗙偣鍜屾櫘閫氶珮涓暟瀛︾煡璇嗙偣鏈夊緢澶х殑鍖哄埆锛岃亴楂樻暟瀛︾敱鐐癸紝娉曞紡鐩寸嚎鏂圭▼锛岃屾櫘閫氶珮涓暟瀛︽病鏈夈傜浉瀵...
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绛旓細鑱岄珮鏁板鍜屾櫘楂樻暟瀛﹀苟娌℃湁浠讳綍鐨勫尯鍒紝濡傛灉璇村皬缂栬冧笉涓婇珮涓殑璇濓紝灏变細閫夋嫨鍘昏亴楂樹笂瀛︺傚叾瀹烇紝鑱岄珮涓婂骞朵笉鏄竴浠堕潪甯镐涪浜虹殑浜嬫儏锛屽鏋滆浣犺兘澶熻鐪熺殑鍘昏繘琛屽涔犵殑璇濓紝閭ｄ箞锛屽湪鑱岄珮褰撲腑锛屼篃鏄兘澶熼棷鍑轰竴鐗囧ぉ銆傚鏋滀綘涓嶈鐪熺殑瀛︿範锛岄偅涔堬紝鍗充娇鏄湪鏅珮褰撲腑锛屼篃骞朵笉浼氳瀛︿範鐨勬垚缁╁彉濂姐傚鏍＄殑褰卞搷鍔涘叾瀹...
