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$\displaystyle F(x)= -\cos x + \sqrt3\sin x$
So, let $\displaystyle F(x) = A\cos(x+w)$. Then:$\displaystyle -\cos x + \sqrt3\sin x=A\cos(x+w)$
$\displaystyle =A\cos x \cos w - A\sin x\sin w$
Compare coefficients of $\displaystyle \cos x$ and $\displaystyle \sin x$:$\displaystyle -1 = A\cos w$
$\displaystyle \sqrt3 = -A\sin w$
Square and add:$\displaystyle 4 = A^2(\cos^2w+\sin^2w)$
$\displaystyle \Rightarrow A = -2$ (taking - sign)
Divide second equation by the first:$\displaystyle \tan w = \sqrt3$
$\displaystyle \Rightarrow w = \pi/3$
$\displaystyle \Rightarrow F(x) = -2\cos(x+\pi/3)$
Grandad