若f(x)=asin(x+π/4)-根号6cos(x+π/3),当a为何值时,函数是偶函数?何时是奇函数
问题描述:
若f(x)=asin(x+π/4)-根号6cos(x+π/3),当a为何值时,函数是偶函数?何时是奇函数
答
f(x)=asin(x+π/4)-根号6cos(x+π/3)
=(√2/2)asinx+)(√2/2)acosx-)=(√2/2)cosx+(3√2/2)sinx,
由 f(x)=f(-x) 得
(√2/2)asinx+(3√2/2)sinx
=-(√2/2)asinx-(3√2/2)sinx,移项,整理得
√2asinx=-3√2sinx,得a=-3