sinx cosx thanx cotx 当x等于0时分别等于多少？ sinxcosx等于什么 求详细

\u5f53x\u8d8b\u4e8e0\u65f6 (cosx-cotx)/x\u6781\u9650\u662f\u591a\u5c11\uff1f\uff08\u8fc7\u7a0b\uff09

\u6c42\u6781\u9650x➔0lim(cosx-cotx)/x\uff1b\u3010\u6ce8\u610f\uff1a\u8fd9\u4e0d\u662f0/0\u578b\uff0c\u4e0d\u80fd\u7528\u7f57\u5fc5\u8fbe\u6cd5\u5219\u3011
\u89e3\uff1a\u539f\u5f0f\uff1dx➔0lim[(sincosx-cosx)/(xsinx)=-\u221e

(1/2)sin2x\u3002
\u4e00\u3001\u4f9d\u636e\uff1a\u500d\u89d2\u516c\u5f0f\uff1a
sin2x=2sinxcosx
\u4e8c\u3001\u500d\u89d2\u516c\u5f0f\u63a8\u5bfc\uff1a
\u56e0\u4e3asin(A+B)=sinAcosB+cosAsinB\uff08\u4e09\u89d2\u51fd\u6570\uff09
\u6240\u4ee5sin2A=2sinAcosA
\u4e09\u3001\u6ce8\uff1a\u4e09\u89d2\u51fd\u6570\u7684\u63a8\u5bfc\uff1a
\u9996\u5148\u5efa\u7acb\u76f4\u89d2\u5750\u6807\u7cfb,\u5728\u76f4\u89d2\u5750\u6807\u7cfbxOy\u4e2d\u4f5c\u5355\u4f4d\u5706O,\u5e76\u4f5c\u51fa\u89d2a,b,\u4e0e-b,\u4f7f\u89d2a\u7684\u5f00\u8fb9\u4e3aOx,\u4ea4\u5706O\u4e8e\u70b9P1,\u7ec8\u8fb9\u4ea4\u5706O\u4e8e\u70b9P2,\u89d2b\u7684\u59cb\u8fb9\u4e3aOP2,\u7ec8\u8fb9\u4ea4\u5706O\u4e8e\u70b9P3,\u89d2-b\u7684\u59cb\u8fb9\u4e3aOP1,\u7ec8\u8fb9\u4ea4\u5706O\u4e8e\u70b9P4.\u8fd9\u65f6P1,P2,P3,P4\u7684\u5750\u6807\u5206\u522b\u4e3a\uff1a
P1\uff081,0\uff09
P2(cosa,sina)
P3(cos(a+b),sin(a+b))
P4(cos(-b),sin(-b))
\u7531P1P3=P2P4\u53ca\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\u5f97\uff1a
^2\u8868\u793a\u5e73\u65b9
[cos(a+b)-1]^2+sin^2(a+b)
=[cos(-b)-cosa]^2+[sin(-b)-sina]^2
\u5c55\u5f00\u6574\u7406\u5f97
2-2cos(a+b)
=2-2(cosacosb-sinasinb)
\u6240\u4ee5cos(a+b)=cosacosb-sinasinb
\u6839\u636e\u8bf1\u5bfc\u516c\u5f0fsin(\u03c0/2-a)=cosa
\u5f97sin(a+b)=cos[\u03c0/2-(a+b)]=sinacosb+cosasinb
\u6269\u5c55\u8d44\u6599\uff1a
\u4e00\u3001\u5e38\u7528\u500d\u89d2\u516c\u5f0f\uff1a
\u2460\u4e8c\u500d\u89d2\u516c\u5f0f\uff1a
sin2\u03b1=2sin\u03b1cos\u03b1
cos2\u03b1=(cos\u03b1)^2-(sin\u03b1)^2=1-2(sin\u03b1)^2=2(cos\u03b1)^2-1
tan2\u03b1=2tan\u03b1/[1-(tan\u03b1)^2]
\u5176\u4ed6\u500d\u89d2\u516c\u5f0f\uff1a
\u2461\u4e09\u500d\u89d2\u516c\u5f0f\uff1a
sin3\u03b1=3sin\u03b1-4sin^3 \u03b1=4sin\u03b1\u00b7sin\uff08\u03c0/3+\u03b1\uff09sin\uff08\u03c0/3-\u03b1\uff09
cos3\u03b1=4cos^3 \u03b1-3cos\u03b1=4cos\u03b1\u00b7cos\uff08\u03c0/3+\u03b1\uff09cos\uff08\u03c0/3-\u03b1\uff09
tan3\u03b1=tan\uff08\u03b1\uff09*(-3+tan\uff08\u03b1\uff09^2\uff09/(-1+3*tan\uff08\u03b1\uff09^2\uff09=tan a \u00b7 tan\uff08\u03c0/3+a\uff09\u00b7 tan\uff08\u03c0/3-\u03b1)
\u4e8c\u3001\u4e09\u89d2\u51fd\u6570\u7684\u6982\u5ff5\uff1a
\u4e09\u89d2\u51fd\u6570\u662f\u6570\u5b66\u4e2d\u5c5e\u4e8e\u521d\u7b49\u51fd\u6570\u4e2d\u7684\u8d85\u8d8a\u51fd\u6570\u7684\u4e00\u7c7b\u51fd\u6570\u3002\u5b83\u4eec\u7684\u672c\u8d28\u662f\u4efb\u4f55\u89d2\u7684\u96c6\u5408\u4e0e\u4e00\u4e2a\u6bd4\u503c\u7684\u96c6\u5408\u7684\u53d8\u91cf\u4e4b\u95f4\u7684\u6620\u5c04\u3002\u901a\u5e38\u7684\u4e09\u89d2\u51fd\u6570\u662f\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u5b9a\u4e49\u7684\u3002\u5176\u5b9a\u4e49\u57ce\u4e3a\u6574\u4e2a\u5b9e\u6570\u57df\u3002
\u4e09\u89d2\u51fd\u6570\u770b\u4f3c\u5f88\u591a\uff0c\u5f88\u590d\u6742\uff0c\u4f46\u53ea\u8981\u638c\u63e1\u4e86\u4e09\u89d2\u51fd\u6570\u7684\u672c\u8d28\u53ca\u5185\u90e8\u89c4\u5f8b\u5c31\u4f1a\u53d1\u73b0\u4e09\u89d2\u51fd\u6570\u5404\u4e2a\u516c\u5f0f\u4e4b\u95f4\u6709\u5f3a\u5927\u7684\u8054\u7cfb\u3002\u800c\u638c\u63e1\u4e09\u89d2\u51fd\u6570\u7684\u5185\u90e8\u89c4\u5f8b\u53ca\u672c\u8d28\u4e5f\u662f\u5b66\u597d\u4e09\u89d2\u51fd\u6570\u7684\u5173\u952e\u6240\u5728\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1-\u500d\u89d2\u516c\u5f0f

当X=0时，SINX=0，COSX=1，TANX=0，C0TX等于TANX的倒数当然也就是等于0

sin0=0,sinx周期是2π
cos0=1,cosx周期是2π
tan0=0,tanx周期是π
cot0=不存在,cotx周期是π

扩展阅读：sin π α ... sec ... 1-cosx ... tan sec csc之间的运算 ... x π arcsiny ... cos x+π ... xsinx的极限 ... a 1-sinθ ... tanx ...