反三角函数

f(x)=sin(x) 的逆函数 y=asin(x)，定义域[-1,1]，值域[-pi/2, pi/2]+n*pi, n=0

g(x)=cos(x) 的逆函数 y=acos(x)，定义域[-1,1]，值域[0, pi]+n*pi, n=0

t(x)=tan(x) 的逆函数 y=atan(x)，定义域R，值域[-pi/2, pi/2]+n*pi, n=0

 

基本关系式: sin(x)=cos(pi/2-x), sin(x)^2+cos(x)^2=1, tan(x/2)=sin(x)/(1+cos(x))

cos(acos(x))=x, sin(asin(x)=x, tan(atan(x))=x

复合函数，取定义域[0, pi/2]

sin(acos(x)) = sqrt(1-cos(acos(x))^2)=sqrt(1-x^2)

cos(asin(x)) = sqrt(1-sin(asin(x))^2)=sqrt(1-x^2)

 

tan(asin(x))=sin(asin(x))/cos(asin(x))=x/sqrt(1-x^2)

 

asin(cos(x))=y, cos(x)=sin(y), y=pi/2-x

acos(sin(x))=y, sin(x)=cos(y), y=pi/2-x

asin(tan(x))=?