# Thread: reducing trig functions to a single function

1. ## reducing trig functions to a single function

Hi
I'm trying to reduce a function in the form
Acos(x)+Bsin(x)
to a single function.
I know that to do this you need to multiply and divide by sqrt(A^2+B^2), but I don't know where to go from there. Can anyone help with this?

2. Originally Posted by Defiant
Hi
I'm trying to reduce a function in the form
Acos(x)+Bsin(x)
to a single function.
I know that to do this you need to multiply and divide by sqrt(A^2+B^2), but I don't know where to go from there. Can anyone help with this?
$\displaystyle \sqrt{A^2 + B^2} \left(\frac{A}{\sqrt{A^2 + B^2}} \cos x + \frac{B}{\sqrt{A^2 + B^2}} \sin x \right)$

Now define $\displaystyle \tan \phi = \frac{A}{B}$ and use the compound angle formula. You get $\displaystyle \sqrt{A^2 + B^2} \sin (x + \phi)$.

3. Thanks alot...kinda stupid, that was the only thing my entire DE was stuck on...