\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u516c\u5f0f
\nsin \u03b1=\u2220\u03b1\u7684\u5bf9\u8fb9 \/ \u659c\u8fb9
\ncos \u03b1=\u2220\u03b1\u7684\u90bb\u8fb9 \/ \u659c\u8fb9
\ntan \u03b1=\u2220\u03b1\u7684\u5bf9\u8fb9 \/ \u2220\u03b1\u7684\u90bb\u8fb9
\ncot \u03b1=\u2220\u03b1\u7684\u90bb\u8fb9 \/ \u2220\u03b1\u7684\u5bf9\u8fb9<\/p>\n
\u500d\u89d2\u516c\u5f0f<\/p>\n
Sin2A=2SinA?CosA
\nCos2A=CosA^2-SinA^2=1-2SinA^2=2CosA^2-1
\ntan2A=\uff082tanA\uff09\/\uff081-tanA^2\uff09
\n\uff08\u6ce8\uff1aSinA^2 \u662fsinA\u7684\u5e73\u65b9 sin2\uff08A\uff09 \uff09
\n\u4e09\u500d\u89d2\u516c\u5f0f
\nsin3\u03b1=4sin\u03b1\u00b7sin(\u03c0\/3+\u03b1)sin(\u03c0\/3-\u03b1)
\ncos3\u03b1=4cos\u03b1\u00b7cos(\u03c0\/3+\u03b1)cos(\u03c0\/3-\u03b1)
\ntan3a = tan a \u00b7 tan(\u03c0\/3+a)\u00b7 tan(\u03c0\/3-a)
\n\u4e09\u500d\u89d2\u516c\u5f0f\u63a8\u5bfc
\nsin3a
\n=sin(2a+a)
\n=sin2acosa+cos2asina
\n\u8f85\u52a9\u89d2\u516c\u5f0f
\nAsin\u03b1+Bcos\u03b1=(A^2+B^2)^(1\/2)sin(\u03b1+t)\uff0c\u5176\u4e2d
\nsint=B\/(A^2+B^2)^(1\/2)
\ncost=A\/(A^2+B^2)^(1\/2)
\ntant=B\/A
\nAsin\u03b1+Bcos\u03b1=(A^2+B^2)^(1\/2)cos(\u03b1-t)\uff0ctant=A\/B
\n\u964d\u5e42\u516c\u5f0f
\nsin^2(\u03b1)=(1-cos(2\u03b1))\/2=versin(2\u03b1)\/2
\ncos^2(\u03b1)=(1+cos(2\u03b1))\/2=covers(2\u03b1)\/2
\ntan^2(\u03b1)=(1-cos(2\u03b1))\/(1+cos(2\u03b1))
\n\u63a8\u5bfc\u516c\u5f0f
\ntan\u03b1+cot\u03b1=2\/sin2\u03b1
\ntan\u03b1-cot\u03b1=-2cot2\u03b1
\n1+cos2\u03b1=2cos^2\u03b1
\n1-cos2\u03b1=2sin^2\u03b1
\n1+sin\u03b1=(sin\u03b1\/2+cos\u03b1\/2)^2
\n=2sina(1-sin²a)+(1-2sin²a)sina
\n=3sina-4sin³a
\ncos3a
\n=cos(2a+a)
\n=cos2acosa-sin2asina
\n=(2cos²a-1)cosa-2(1-sin²a)cosa
\n=4cos³a-3cosa
\nsin3a=3sina-4sin³a
\n=4sina(3\/4-sin²a)
\n=4sina[(\u221a3\/2)²-sin²a]
\n=4sina(sin²60\u00b0-sin²a)
\n=4sina(sin60\u00b0+sina)(sin60\u00b0-sina)
\n=4sina*2sin[(60+a)\/2]cos[(60\u00b0-a)\/2]*2sin[(60\u00b0-a)\/2]cos[(60\u00b0-a)\/2]
\n=4sinasin(60\u00b0+a)sin(60\u00b0-a)
\ncos3a=4cos³a-3cosa
\n=4cosa(cos²a-3\/4)
\n=4cosa[cos²a-(\u221a3\/2)²]
\n=4cosa(cos²a-cos²30\u00b0)
\n=4cosa(cosa+cos30\u00b0)(cosa-cos30\u00b0)
\n=4cosa*2cos[(a+30\u00b0)\/2]cos[(a-30\u00b0)\/2]*{-2sin[(a+30\u00b0)\/2]sin[(a-30\u00b0)\/2]}
\n=-4cosasin(a+30\u00b0)sin(a-30\u00b0)
\n=-4cosasin[90\u00b0-(60\u00b0-a)]sin[-90\u00b0+(60\u00b0+a)]
\n=-4cosacos(60\u00b0-a)[-cos(60\u00b0+a)]
\n=4cosacos(60\u00b0-a)cos(60\u00b0+a)
\n\u4e0a\u8ff0\u4e24\u5f0f\u76f8\u6bd4\u53ef\u5f97
\ntan3a=tanatan(60\u00b0-a)tan(60\u00b0+a)
\n\u534a\u89d2\u516c\u5f0f
\ntan(A\/2)=(1-cosA)\/sinA=sinA\/(1+cosA);
\ncot(A\/2)=sinA\/(1-cosA)=(1+cosA)\/sinA.
\nsin^2(a\/2)=(1-cos(a))\/2
\ncos^2(a\/2)=(1+cos(a))\/2
\ntan(a\/2)=(1-cos(a))\/sin(a)=sin(a)\/(1+cos(a))
\n\u5b66\u4e60\u65b9\u6cd5\u7f51[www.xuexifangfa.com]
\n\u4e09\u89d2\u548c
\nsin(\u03b1+\u03b2+\u03b3)=sin\u03b1\u00b7cos\u03b2\u00b7cos\u03b3+cos\u03b1\u00b7sin\u03b2\u00b7cos\u03b3+cos\u03b1\u00b7cos\u03b2\u00b7sin\u03b3-sin\u03b1\u00b7sin\u03b2\u00b7sin\u03b3
\ncos(\u03b1+\u03b2+\u03b3)=cos\u03b1\u00b7cos\u03b2\u00b7cos\u03b3-cos\u03b1\u00b7sin\u03b2\u00b7sin\u03b3-sin\u03b1\u00b7cos\u03b2\u00b7sin\u03b3-sin\u03b1\u00b7sin\u03b2\u00b7cos\u03b3
\ntan(\u03b1+\u03b2+\u03b3)=(tan\u03b1+tan\u03b2+tan\u03b3-tan\u03b1\u00b7tan\u03b2\u00b7tan\u03b3)\/(1-tan\u03b1\u00b7tan\u03b2-tan\u03b2\u00b7tan\u03b3-tan\u03b3\u00b7tan\u03b1)
\n\u4e24\u89d2\u548c\u5dee
\ncos(\u03b1+\u03b2)=cos\u03b1\u00b7cos\u03b2-sin\u03b1\u00b7sin\u03b2
\ncos(\u03b1-\u03b2)=cos\u03b1\u00b7cos\u03b2+sin\u03b1\u00b7sin\u03b2
\nsin(\u03b1\u00b1\u03b2)=sin\u03b1\u00b7cos\u03b2\u00b1cos\u03b1\u00b7sin\u03b2
\ntan(\u03b1+\u03b2)=(tan\u03b1+tan\u03b2)\/(1-tan\u03b1\u00b7tan\u03b2)
\ntan(\u03b1-\u03b2)=(tan\u03b1-tan\u03b2)\/(1+tan\u03b1\u00b7tan\u03b2)
\n\u548c\u5dee\u5316\u79ef
\nsin\u03b8+sin\u03c6 = 2 sin[(\u03b8+\u03c6)\/2] cos[(\u03b8-\u03c6)\/2]
\nsin\u03b8-sin\u03c6 = 2 cos[(\u03b8+\u03c6)\/2] sin[(\u03b8-\u03c6)\/2]
\ncos\u03b8+cos\u03c6 = 2 cos[(\u03b8+\u03c6)\/2] cos[(\u03b8-\u03c6)\/2]
\ncos\u03b8-cos\u03c6 = -2 sin[(\u03b8+\u03c6)\/2] sin[(\u03b8-\u03c6)\/2]
\ntanA+tanB=sin(A+B)\/cosAcosB=tan(A+B)(1-tanAtanB)
\ntanA-tanB=sin(A-B)\/cosAcosB=tan(A-B)(1+tanAtanB)
\n\u79ef\u5316\u548c\u5dee
\nsin\u03b1sin\u03b2 = [cos(\u03b1-\u03b2)-cos(\u03b1+\u03b2)] \/2
\ncos\u03b1cos\u03b2 = [cos(\u03b1+\u03b2)+cos(\u03b1-\u03b2)]\/2
\nsin\u03b1cos\u03b2 = [sin(\u03b1+\u03b2)+sin(\u03b1-\u03b2)]\/2
\ncos\u03b1sin\u03b2 = [sin(\u03b1+\u03b2)-sin(\u03b1-\u03b2)]\/2
\n\u8bf1\u5bfc\u516c\u5f0f
\nsin(-\u03b1) = -sin\u03b1
\ncos(-\u03b1) = cos\u03b1
\ntan (\u2014a)=-tan\u03b1
\nsin(\u03c0\/2-\u03b1) = cos\u03b1
\ncos(\u03c0\/2-\u03b1) = sin\u03b1
\nsin(\u03c0\/2+\u03b1) = cos\u03b1
\ncos(\u03c0\/2+\u03b1) = -sin\u03b1
\nsin(\u03c0-\u03b1) = sin\u03b1
\ncos(\u03c0-\u03b1) = -cos\u03b1
\nsin(\u03c0+\u03b1) = -sin\u03b1
\ncos(\u03c0+\u03b1) = -cos\u03b1
\ntanA= sinA\/cosA
\ntan\uff08\u03c0\/2\uff0b\u03b1\uff09\uff1d\uff0dcot\u03b1
\ntan\uff08\u03c0\/2\uff0d\u03b1\uff09\uff1dcot\u03b1
\ntan\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1
\ntan\uff08\u03c0\uff0b\u03b1\uff09\uff1dtan\u03b1
\n\u8bf1\u5bfc\u516c\u5f0f\u8bb0\u80cc\u8bc0\u7a8d\uff1a\u5947\u53d8\u5076\u4e0d\u53d8\uff0c\u7b26\u53f7\u770b\u8c61\u9650
\n\u4e07\u80fd\u516c\u5f0f
\nsin\u03b1=2tan(\u03b1\/2\uff09\/\uff3b1+tan\uff3e(\u03b1\/2)\uff3d
\ncos\u03b1=\uff3b1-tan\uff3e(\u03b1\/2)\uff3d\/1+tan\uff3e(\u03b1\/2)\uff3d
\ntan\u03b1=2tan(\u03b1\/2)\/\uff3b1-tan\uff3e(\u03b1\/2)\uff3d
\n\u5176\u5b83\u516c\u5f0f
\n(1)(sin\u03b1)^2+(cos\u03b1)^2=1
\n(2)1+(tan\u03b1)^2=(sec\u03b1)^2
\n(3)1+(cot\u03b1)^2=(csc\u03b1)^2
\n\u8bc1\u660e\u4e0b\u9762\u4e24\u5f0f,\u53ea\u9700\u5c06\u4e00\u5f0f,\u5de6\u53f3\u540c\u9664(sin\u03b1)^2,\u7b2c\u4e8c\u4e2a\u9664(cos\u03b1)^2\u5373\u53ef
\n(4)\u5bf9\u4e8e\u4efb\u610f\u975e\u76f4\u89d2\u4e09\u89d2\u5f62,\u603b\u6709
\ntanA+tanB+tanC=tanAtanBtanC
\n\u8bc1:
\nA+B=\u03c0-C
\ntan(A+B)=tan(\u03c0-C)
\n(tanA+tanB)\/(1-tanAtanB)=(tan\u03c0-tanC)\/(1+tan\u03c0tanC)
\n\u6574\u7406\u53ef\u5f97
\ntanA+tanB+tanC=tanAtanBtanC
\n\u5f97\u8bc1
\n\u540c\u6837\u53ef\u4ee5\u5f97\u8bc1,\u5f53x+y+z=n\u03c0(n\u2208Z)\u65f6,\u8be5\u5173\u7cfb\u5f0f\u4e5f\u6210\u7acb
\n\u7531tanA+tanB+tanC=tanAtanBtanC\u53ef\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba
\n(5)cotAcotB+cotAcotC+cotBcotC=1
\n(6)cot(A\/2)+cot(B\/2)+cot(C\/2)=cot(A\/2)cot(B\/2)cot(C\/2)
\n(7)(cosA\uff09^2+(cosB\uff09^2+(cosC\uff09^2=1-2cosAcosBcosC
\n(8)\uff08sinA\uff09^2+\uff08sinB\uff09^2+\uff08sinC\uff09^2=2+2cosAcosBcosC
\n(9)sin\u03b1+sin(\u03b1+2\u03c0\/n)+sin(\u03b1+2\u03c0*2\/n)+sin(\u03b1+2\u03c0*3\/n)+\u2026\u2026+sin[\u03b1+2\u03c0*(n-1)\/n]=0
\ncos\u03b1+cos(\u03b1+2\u03c0\/n)+cos(\u03b1+2\u03c0*2\/n)+cos(\u03b1+2\u03c0*3\/n)+\u2026\u2026+cos[\u03b1+2\u03c0*(n-1)\/n]=0 \u4ee5\u53ca
\nsin^2(\u03b1)+sin^2(\u03b1-2\u03c0\/3)+sin^2(\u03b1+2\u03c0\/3)=3\/2
\ntanAtanBtan(A+B)+tanA+tanB-tan(A+B)=0<\/p>\n","protected":false},"excerpt":{"rendered":"
\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u516c\u5f0f sin \u03b1=\u2220\u03b1\u7684\u5bf9\u8fb9 \/ \u659c\u8fb9 cos \u03b1=\u2220\u03b1\u7684\u90bb\u8fb9 \/ \u659c\u8fb9 tan \u03b1=\u2220\u03b1\u7684\u5bf9\u8fb9 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/600"}],"collection":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/comments?post=600"}],"version-history":[{"count":1,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/600\/revisions"}],"predecessor-version":[{"id":601,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/600\/revisions\/601"}],"wp:attachment":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/media?parent=600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/categories?post=600"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/tags?post=600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}