Question

求函数的值。

f(x)=sin(x+π/4)+2sin(x-π/4）-4cos2x+3cos（x+(3π)/4）
(1)x=π/4
(2)x=(3π)/4
不会化简阿，sin和cos之间怎么弄？求过程。

Answer 1

f(π/4)=sin(π/2)+2sin(0）-4cosπ/2+3cos（π）=1+0-0+-3=-2
f【(3π)/4】=sin(π)+2sin(π/2）-4cos(3π)/2+3cos(3π)/2=0+2-0+0=2

Answer 2

（1）f(π/4)=sin(π/2）+2sin(0)-4cos(π/2)+3cos(π)
=1 +0 -0 +3(-1)
=-2
（2）f(3π/4)=sin(π）+2sin(π/2)-4cos(6π/4)+3cos(6π/4)
=0 +2 -0 +0
=2