# find the period of a trigonometric function

I've found the period of this trigonometric function, $$y=\sin^n(x)+\cos^n(x)$$.

when n （$n\neq2$）is odd, the period is $2\pi$,

when n is even, the period is $\frac{\pi}{2}$.

but how to proof it?

• What about when $n=2$? – Mike Apr 24 '14 at 10:29
• This can easily be generalized for $\sin^ax+\cos^bx$. – Lucian Apr 24 '14 at 11:20