题目

函数y=sin[2(x-π/3)＋φ]是偶函数,切0＜φ＜π,则φ=

提问时间：2020-10-12

答案

y=sin[2(x-π/3)＋φ]是偶函数
则f(-x)=f(x)
sin[2(-x-π/3)＋φ]=sin[2(x-π/3)＋φ]
sin[-2x-2π/3＋φ]=sin[2x-π/3＋φ]
sin[-2x-2π/3＋φ]-sin[2x-2π/3＋φ]
=2cos（-2x-2π/3＋φ+2x-π/3＋φ)/2*sin(
-2x-2π/3＋φ-2x+π/3-φ）/2
=0
即（-2x-2π/3＋φ+2x-2π/3＋φ)/2=π/2+kπ
则φ-2π/3=π/2+kπ
φ=π/6+kπ
0＜φ＜π
则φ=π/6