f(x)=sin(2x+3π/2)
=sin(2x+3π/2-2π)
=sin(2x-π/2)
=-sin(π/2-2x)
=-cos2x
f(-x)=-cos(-2x)=-cos2x=f(x)
且定义域是R
关于原点对称
所以是偶函数