Question

已知函数f(x)=Sinx+Sin(x+90°),x∈R.⑴.求f(x)的最小正周期.⑵.求f(x)的最大值和最小值.

Answer 1

f(x)=Sinx+Sin(x+90°)=sinx +cosx =√2 *sun(x+ 45)

(1)最小正周期T=2pi

(2)最大值是：=√2.最小值= - √2

f(a)=sina + cosa = 3/4 平方：

sin^2a +cos^2a +2sina*cosa = 9/16

2sina*cosa = - 7/16

sin2a = -7/16