# Math Help - change to the form Acos(x+w)

1. ## change to the form Acos(x+w)

How do you change F(x) = -cosx + sqrt3sint to the form:

Acos(x+w)

with A and w both exact values?

2. Hello JQ2009
Originally Posted by JQ2009
How do you change F(x) = -cosx + sqrt3sint to the form:

Acos(x+w)

with A and w both exact values?
I assume you mean
$F(x)= -\cos x + \sqrt3\sin x$
So, let $F(x) = A\cos(x+w)$. Then:
$-\cos x + \sqrt3\sin x=A\cos(x+w)$
$=A\cos x \cos w - A\sin x\sin w$
Compare coefficients of $\cos x$ and $\sin x$:
$-1 = A\cos w$

$\sqrt3 = -A\sin w$
$4 = A^2(\cos^2w+\sin^2w)$
$\Rightarrow A = -2$ (taking - sign)
$\tan w = \sqrt3$
$\Rightarrow w = \pi/3$
$\Rightarrow F(x) = -2\cos(x+\pi/3)$