Proving <sin^2(k*r-wt)>= 1/2 using Time Average Integral Method

[aakeso1]

Homework Statement

Show that <sin^2(k*r-wt)>= 1/2

Homework Equations

<f(t)>= 1/T integral ( f(t')dt' ) from [t, t+T]

The Attempt at a Solution

 

[Svein]

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

 

[aakeso1]

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

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

 

[Ray Vickson]

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

Try it and see!

 

[Svein]

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

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