函数y=sin2x(sin2x+cos2x)的周期是如题,要过程的啦,然后答案是派/2.谢谢._数学解答

函数y=sin2x(sin2x+cos2x)的周期是
如题,要过程的啦,然后答案是派/2.谢谢.

人气：421 ℃　时间：2020-05-12 07:44:19

解答

y=sin²2x+sin2xcos2x
=(1-cos4x)/2+1/2*sin4x
=√2/2(sin4x*√2/2-cos4x*√2/2)+1/2
=√2/2(sin4xcosπ/4-cos4xπ/4)+1/2
=√2/2*sin(4x+π/4)+1/2
所以T=2π/4=π/2