Question

Show: Acos(wt) + B sin(wt) = rsin(wt - theta)

Answer 1

Sine Angle Difference Formula:\[\large\rm \color{royalblue}{\sin(C-D)=\sin C \cos D-\sin D \cos C}\]

Applying this gives us:\[\large\rm r \sin\left(\omega t-\theta\right)=r\left[\sin(\omega t)\cos \theta-\sin \theta \cos(\omega t)\right]\]Distributing the r,\[\large\rm =\color{orangered}{r \cos \theta}\sin(\omega t)+\color{red}{(-r\sin \theta)} \cos(\omega t)\]
So maybe you can see what's going on,
Your identity holds true when
r*cos(theta)=B
-r*sin(theta)=A\[\large\rm =\color{orangered}{B}\sin(\omega t)+\color{red}{A} \cos(\omega t)\]

Answer 2

Any more information? :o
Does that help maybe?

Answer 3

Ok i see what you did, but I'm still stuck on what do do next :(

Answer 4

Oh wait, nvm