# Time Average integral

1. Sep 15, 2015

### aakeso1

• Member warned about posting with no effort
1. The problem statement, all variables and given/known data

Show that <sin^2(k*r-wt)>= 1/2
2. Relevant equations
<f(t)>= 1/T integral ( f(t')dt' ) from [t, t+T]

3. The attempt at a solution

2. Sep 15, 2015

### Svein

Trigonometric identities: You know that $\cos(2x)=\cos^{2}(x)-\sin^{2}(x)=1-2\sin^{2}(x)$?

3. Sep 15, 2015

### aakeso1

Right, so I use the appropriate identity ( 1-2sin^2(x) ), and carry out the integration?

4. Sep 15, 2015

### Ray Vickson

Try it and see!

5. Sep 15, 2015

### Svein

Well, I do not know exactly what you mean, but solve the identity for sin2(x) and integrate (for example from 0 to 2π).