Total power contained in 10.0[cos(160.7*pi*t)]^4 (Fourier Series)

[Jd303]

Homework Statement

Compute the power contained in the periodic signal x(t) = 10.0[cos(160.7*pi*t)]^4

Homework Equations

The Attempt at a Solution

Hey guys,
I have just started Fourier Series and am struggling with this one. Without writing all my calculations, -I start with inverse Euler formula.
-Then integrate x(t)*e^(-j*ω*k*t) with respect to t. From 0 to (To)
-Then consider the value of the final exponentials when k is an odd and even number.

However i calculate that the answer for ak for any value of k to be 15/4?

Once again I have only started Fourier recently so any direction would be much appreciated.

 

[vela]

Please show your work.

Another approach you might try is using trig identities to find the Fourier series.

 

[Jd303]

Provided are my calculations in the attachment
-The function has already been converted using the inverse Euler formula
- σ is equal to 160.7*pi*t
- The fundamental frequency is 2*σ/(2*π)

-Anyway to calculate this equation is fine, inverse euler was just given as a suggestion to begin.