# Periods of Powers of Trigonometric Functions

1. Aug 18, 2010

### Shaggy16

1. The problem statement, all variables and given/known data
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)?

2. Relevant equations

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 18, 2010

### 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..

3. Aug 18, 2010

### vela

Staff Emeritus
Use trig identities for sin2 x and cos2 x.

4. Aug 18, 2010

### Shaggy16

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