Periods of Powers of Trigonometric Functions

[Shaggy16]

Homework Statement

Is there a way to determine the period of a function like f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x)?

Homework Equations

The Attempt at a Solution

I know how to find the periods of sines, cosines, and arbitrary sums of the two, but the introduction of exponents has me at a complete loss. Please don't show me how; just point me in the general direction.

 

[theJorge551]

I only have a basic knowledge of trigonometric functions, but without any other indicator of how to approach this I'd put in arbitrary values for the constants a, b, c, d, e, f, g, and h, graph the function, and it seems like you'd be able to derive a method of finding arbitrary periodic sums. Just a thought..

 

[vela]

Use trig identities for sin² x and cos² x.

 

[Shaggy16]

I forgot all about the half-angle identities... Thank you