Question

已知函数f(x)＝sin(x＋θ)＋3cos(x＋θ)θ∈－π2，π2是偶函数，...

已知函数f(x)＝sin(x＋θ)＋3cos(x＋θ)θ∈－π2，π2是偶函数，则θ的值为________．

Answer 1

θ＝π/6
(回顾检验法)据已知可得f(x)＝2sinx＋θ＋π3，若函数为偶函数，则必有θ＋π3＝kπ＋π2(k∈Z)，又由于θ∈－π2，π2，故有θ＋π3＝π2，解得θ＝π/6，经代入检验符合题意．