How to average cos2q:
Addition formula for cosine:
- cos(A+B) = cosAcosB - sinAsinB
- For A=B=q, cos(2q) = cos2q - sin2q
- Furthermore cos2q + sin2q = 1 so
- cos2q = cos2q - (1 - cos2q) = 2cos2q - 1
- Therefore cos2q = (1 + cos2q) / 2
This gives us the tools we need to integrate cos2q over an interval.
In general over an interval (a,b) is