Question

f(cosx)=cos5x,则f(sinx)=

Answer 1

解:因为f(cosx)=cos5x,所以f(0)=0,f(1/2)=1/2,f(√2/2)=-√2/2,f(√3/2)=-√3/2,f(1)=1,由数据可知,所以f(sinx)=sin5x

Answer 2

解：
因为f(cosx)=cos5x
故
f(cos(π/2－x))
=cos[5(π/2－x)]
=cos(5π/2－5x)
=sin5x
即
f(sinx)=sin5x