Y=sin(pai/4+x)cos(pai/4+x)是奇函数还是偶函数?周期是多少?

Question

Y=sin(pai/4+x)cos(pai/4+x)是奇函数还是偶函数?周期是多少?

Answer 1

y=1/2*[2sin(π/4+x)cos(π/4+x)]
=1/2*sin[2(π/4+x)]
=1/2*sin(π/2+2x)
=1/2*cos2x
所以这是偶函数
T=2π/2=π