Question

已知函数f(x)=sinx/2cosx/2+cos平方x/2-1/2

(1)若f(a)=√2/4,a∈(0,π),求a的值
(2)求函数f(x)在[-π/4,π]上的最大值和最小值
正确过程。。

Answer 1

1、
f(x)=1/2*sinx+(1+cosx)/2-1/2
=1/2(sinx+cosx)
=(√2/2)(sinx*√2/2+cosx*√2/2)
=(√2/2)(sinxcosπ/4+cosxsinπ/4)
=(√2/2)sin(x+π/4)

f(a)=(√2/2)sin(a+π/4)=√2/4
sin(a+π/4)=1/2
π/4<a+π/4<5π/4
所以a+π/4=5π/6
a=7π/12

2、
-π/4<=x<=π
0<=x+π/4<=5π/4
所以x+π/4=5π/4，sin(x+π/4)最小=-√2/2
x+π/4=π/2，sin(x+π/4)最大=1
在乘以√2/2
所以最大值=√2/2，最小值=-1/2