当x的值域为[-180,0] 时,求f(x)=sin X-根号3 cos x 的单调区间是
问题描述：
当x的值域为[-180,0] 时,求f(x)=sin X-根号3 cos x 的单调区间是
答
f(x)=1/2[1/2sinx-√3/2cosx]
=1/2[cos60sinx-sin60cosx]
=1/2[sin(x-π/3)]
x-π/3的定义域为[-4π/3,-π/3]
sin(x-π/3)这个正弦图你会画不,就是在x-π/3＝〔－4π/3．－π〕和[-π/2,-π/3]时递增,x-π/3＝〔－π,－π/2〕时递减
所以x=〔－π,－2π/3〕〔－π/6,0〕弟增
x=[-2π/3,-π/6]时弟减