Question

一道函数体求解.已知函数f（x）=sinx+sin(x+∏/2).(1)求f(x的最小正周期；（2)求f（x）的最大值和

Answer 1

f(x)=sinx+cos[π/2-(x+π/2)]

=sinx+cos(-x)

=sinx+cosx

=√2sin(x+π/4)

(1)f(x)的最小正周期T=2π

(2)-√2≤f(x)≤√2

(3)f(a)=sina+cosa=3/4

(sina+cosa)²=(3/4)²

sin²a+cos²a+2sinacosa=9/16

1+sin2a=9/16

sin2a=-7/16