求反三角函数和三角函数的关系 反三角函数和三角函数的转换公式列一下~谢谢了~
\u6c42\u4e09\u89d2\u51fd\u6570\u548c\u53cd\u4e09\u89d2\u51fd\u6570\u5e38\u7528\u516c\u5f0f1\u3001\u4e09\u89d2\u51fd\u6570\u5e38\u7528\u516c\u5f0f
\uff081\uff09\u4e24\u89d2\u548c\u4e0e\u5316\u7684\u516c\u5f0f
sin(A\u00b1B)=sinAcosB\u00b1cosAsinB\uff1bcos(A+B)=cosAcosB-sinAsinB\uff1bcos(A-B)=cosAcosB+sinAsinB\uff1btan(A+B)=(tanA+tanB)/(1-tanA\u00b7tanB)\uff1btan(A-B) =(tanA-tanB)/(1+tanA\u00b7tanB)\u3002
\uff082\uff09\u548c\u5dee\u5316\u79ef\u516c\u5f0f
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]\uff1bsina-sinb=2cos[(a+b)/2]sin[(a-b)/2]\uff1bcosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]\uff1bcosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]\u3002
\uff083\uff09\u79ef\u5316\u548c\u5dee\u516c\u5f0f
sinasinb=-1/2[cos(a+b)-cos(a-b)]\uff1bcosacosb=1/2[cos(a+b)+cos(a-b)]\uff1bsinacosb=1/2 [sin(a+b)+sin(a-b)]\uff1b cosasinb=1/2 [sin(a+b)-sin(a-b)]\u3002
2\u3001\u53cd\u4e09\u89d2\u51fd\u6570\u5e38\u7528\u516c\u5f0f
\uff081\uff09arcsin(-x)=-arcsinx\uff1barccos(-x)=\u03c0-arccosx\uff1barctan(-x)=-arctanx\uff1barccot(-x)=\u03c0-arccotx\u3002
\uff082\uff09arcsinx+arccosx=\u03c0/2=arctanx+arccotx\uff1bsin(arcsinx)=x=cos(arccosx)=tan(arctanx)=cot(arccotx)\u3002
\uff083\uff09\u5f53x\u2208(\u2014\u03c0/2,\u03c0/2)\u65f6\uff0carcsin(sinx)=x\uff1b\u5f53x\u2208(0,\u03c0)\uff0carccos(cosx)=x\uff1bx\u2208(\u2014\u03c0/2,\u03c0/2)\uff0carctan(tanx)=x\uff1bx\u2208(0,\u03c0)\uff0carccot(cotx)=x\u3002
\uff084\uff09\u82e5(arctanx+arctany)\u2208(\u2014\u03c0/2,\u03c0/2)\uff0c\u5219arctanx+arctany=arctan(x+y/1-xy)\u3002
\u6269\u5c55\u8d44\u6599
\u53cd\u4e09\u89d2\u51fd\u6570\u5206\u7c7b
1\u3001\u53cd\u6b63\u5f26\u51fd\u6570
\u6b63\u5f26\u51fd\u6570y=sinx\u5728[-\u03c0/2\uff0c\u03c0/2]\u4e0a\u7684\u53cd\u51fd\u6570\uff0c\u53eb\u505a\u53cd\u6b63\u5f26\u51fd\u6570\u3002\u8bb0\u4f5carcsinx\uff0c\u8868\u793a\u4e00\u4e2a\u6b63\u5f26\u503c\u4e3ax\u7684\u89d2\uff0c\u8be5\u89d2\u7684\u8303\u56f4\u5728[-\u03c0/2\uff0c\u03c0/2]\u533a\u95f4\u5185\u3002\u5b9a\u4e49\u57df[-1\uff0c1]\uff0c\u503c\u57df[-\u03c0/2\uff0c\u03c0/2]\u3002
2\u3001\u53cd\u4f59\u5f26\u51fd\u6570
\u4f59\u5f26\u51fd\u6570y=cosx\u5728[0\uff0c\u03c0]\u4e0a\u7684\u53cd\u51fd\u6570\uff0c\u53eb\u505a\u53cd\u4f59\u5f26\u51fd\u6570\u3002\u8bb0\u4f5carccosx\uff0c\u8868\u793a\u4e00\u4e2a\u4f59\u5f26\u503c\u4e3ax\u7684\u89d2\uff0c\u8be5\u89d2\u7684\u8303\u56f4\u5728[0\uff0c\u03c0]\u533a\u95f4\u5185\u3002\u5b9a\u4e49\u57df[-1\uff0c1]\uff0c\u503c\u57df[0\uff0c\u03c0]\u3002
3\u3001\u53cd\u6b63\u5207\u51fd\u6570
\u6b63\u5207\u51fd\u6570y=tanx\u5728(-\u03c0/2\uff0c\u03c0/2)\u4e0a\u7684\u53cd\u51fd\u6570\uff0c\u53eb\u505a\u53cd\u6b63\u5207\u51fd\u6570\u3002\u8bb0\u4f5carctanx\uff0c\u8868\u793a\u4e00\u4e2a\u6b63\u5207\u503c\u4e3ax\u7684\u89d2\uff0c\u8be5\u89d2\u7684\u8303\u56f4\u5728(-\u03c0/2\uff0c\u03c0/2)\u533a\u95f4\u5185\u3002\u5b9a\u4e49\u57dfR\uff0c\u503c\u57df(-\u03c0/2\uff0c\u03c0/2)\u3002
4\u3001\u53cd\u4f59\u5207\u51fd\u6570
\u4f59\u5207\u51fd\u6570y=cotx\u5728(0\uff0c\u03c0)\u4e0a\u7684\u53cd\u51fd\u6570\uff0c\u53eb\u505a\u53cd\u4f59\u5207\u51fd\u6570\u3002\u8bb0\u4f5carccotx\uff0c\u8868\u793a\u4e00\u4e2a\u4f59\u5207\u503c\u4e3ax\u7684\u89d2\uff0c\u8be5\u89d2\u7684\u8303\u56f4\u5728(0\uff0c\u03c0)\u533a\u95f4\u5185\u3002\u5b9a\u4e49\u57dfR\uff0c\u503c\u57df(0\uff0c\u03c0)\u3002
\u53cd\u6b63\u5272\u51fd\u6570
\u6b63\u5272\u51fd\u6570y=secx\u5728[0\uff0c\u03c0/2)U(\u03c0/2\uff0c\u03c0]\u4e0a\u7684\u53cd\u51fd\u6570\uff0c\u53eb\u505a\u53cd\u6b63\u5272\u51fd\u6570\u3002\u8bb0\u4f5carcsecx\uff0c\u8868\u793a\u4e00\u4e2a\u6b63\u5272\u503c\u4e3ax\u7684\u89d2\uff0c\u8be5\u89d2\u7684\u8303\u56f4\u5728[0\uff0c\u03c0/2)U(\u03c0/2\uff0c\u03c0]\u533a\u95f4\u5185\u3002\u5b9a\u4e49\u57df(-\u221e\uff0c-1]U[1\uff0c+\u221e)\uff0c\u503c\u57df[0\uff0c\u03c0/2)U(\u03c0/2\uff0c\u03c0]\u3002
5\u3001\u53cd\u4f59\u5272\u51fd\u6570
\u4f59\u5272\u51fd\u6570y=cscx\u5728[-\u03c0/2\uff0c0)U(0\uff0c\u03c0/2]\u4e0a\u7684\u53cd\u51fd\u6570\uff0c\u53eb\u505a\u53cd\u4f59\u5272\u51fd\u6570\u3002\u8bb0\u4f5carccscx\uff0c\u8868\u793a\u4e00\u4e2a\u4f59\u5272\u503c\u4e3ax\u7684\u89d2\uff0c\u8be5\u89d2\u7684\u8303\u56f4\u5728[-\u03c0/2\uff0c0)U(0\uff0c\u03c0/2]\u533a\u95f4\u5185\u3002\u5b9a\u4e49\u57df(-\u221e\uff0c-1]U[1\uff0c+\u221e)\uff0c\u503c\u57df[-\u03c0/2\uff0c0)U(0\uff0c\u03c0/2]\u3002
x=arcsint
两者互为反函数
sinx的自变量是角度，arcsinx自变量是三角函数值（定义域是[-1，1]）
sinx的因变量是三角函数值（值域是[-1，1]，sinx因变量是角度
两函数关于直线y=x对称，过点（0，0）
比如y=sinx,那么他的反函数就是x=arcsiny,为了写成一般熟悉的函数的样子改写成y=arcsinx,其实这里面的x就是前面函数的y
y=sinx变换得x=arcsiny，还是同一函数
但对应法则不同，自变量，因变量不同，定义域，值域不同
因有不同，又习惯x表示自变量，y表示因变量
将x，y互换，得y=arcsinx，即为反函数
这不再是同一函数
关于y=x对称
绛旓細sinx=t x=arcsint 涓よ呬簰涓哄弽鍑芥暟 sinx鐨勮嚜鍙橀噺鏄搴︼紝arcsinx鑷彉閲忔槸涓夎鍑芥暟鍊硷紙瀹氫箟鍩熸槸[-1锛1]锛塻inx鐨勫洜鍙橀噺鏄笁瑙掑嚱鏁板硷紙鍊煎煙鏄痆-1锛1]锛宻inx鍥犲彉閲忔槸瑙掑害 涓ゅ嚱鏁板叧浜庣洿绾縴=x瀵圭О锛岃繃鐐癸紙0锛0锛
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