# Trigonometric identity forced oscillations

1. Apr 22, 2007

### Gyroscope

2. Apr 22, 2007

### cristo

Staff Emeritus
Well, you've got an expression that's in the form sinAsinB; so you look to use the formula cos(A-B)=cosAcosB+sinAsinB.

From this, you know that $$\cos\{\omega_it-\phi-\omega t\}=\cos\{\omega_i t-\phi\}\cos(\omega t)+\sin\{\omega_i t-\phi\}\sin(\omega t)$$. You can work out the similar expression that $$\cos\{\omega_it-\phi+\omega t\}=\cos\{\omega_i t-\phi\}\cos(\omega t)-\sin\{\omega_i t-\phi\}\sin(\omega t)$$ Then subtract the second from the first.