## AmTran_Bus one year ago Show c1 sin omega t + c2 cos omega t is equal to A sin (omega t + phi)

1. AmTran_Bus

|dw:1442673851220:dw| The issue is that I do not understand what omega or phi is.

2. ParthKohli

Did you try to compare both equations?

3. ParthKohli

$A\sin(\omega t + \phi)$$= c_1 \sin (\omega t) + c_2 \cos(\omega t)$$= \color{#c00}{A\cos (\phi)} \sin (\omega t) + \color{#C00}{A \sin (\phi)} \cos(\omega t)$

4. anonymous

Basically $\omega,\phi,A$ These 3 quantities are constant while t is variable, so as @ParthKohli has highlighted, the quantity Acos(phi) and Asin(phi) may be clubbed together as a single constant like $C_{1}=A\cos(\phi) \space \space \space ,\space \space \space C_{2}=A\sin(\phi)$