(1)已知f(cosx)=cos17x,求证f(sinx)=sin17x (2)已知f(sinx)=cos17x求f(1\2)的值
问题描述:
(1)已知f(cosx)=cos17x,求证f(sinx)=sin17x (2)已知f(sinx)=cos17x求f(1\2)的值
答
(1),f(sinx)=f[cos(π/2-x)]=cos17(π/2-x)=cos(17π/2-17x)=cos(π/2-17x)=sin17x.
(2),f(sinx)=cos17x,令sinx=1/2,则:x=2kπ+π/6,或x=2kπ+5π/6,(k为整数)
当x=2kπ+π/6时,cos17x=cos(34kπ+17π/6)=cos5π/6=-√3/2;
当x=2kπ+5π/6时,cos17x=cos(34kπ+85π/6)=cosπ/6=√3/2.
所以f(1/2)=√3/2,或-√3/2.