已知f(x)满足f(cosx)=x/2(0≤x≤π),则f(cos(4π/3))= 已知f(x)满足f(cosx)=cos2x,则f(sin15°)的值为
问题描述:
已知f(x)满足f(cosx)=x/2(0≤x≤π),则f(cos(4π/3))= 已知f(x)满足f(cosx)=cos2x,则f(sin15°)的值为
答
f(cos(4π/3))= f(cos(2π/3))= 2π/3/2=π/3
f(sin15°)=f(cos75°)=cos(2*75°)=-(根号3)/2第一题没看明白,麻烦解释一下。利用诱导公式cos(4π/3)=cos(2π-4π/3))= cos(2π/3)这质上是区间转化 ,第(2)是函数名称的转化