Hello Paymemoney Originally Posted by
Paymemoney Hi
Can someone tell me how to do this question:
1) Convert 4sin2x+5cos2x into a single cosine wave form Acos(2x+C)
P.S
Just to expand a little on mathaddict's reply, use the identity$\displaystyle \cos(P+Q) = \cos P \cos Q - \sin P \sin Q$
as follows:$\displaystyle A\cos(2x+C) = 4\sin 2x +5\cos 2x$
$\displaystyle \Rightarrow A\cos2x\cos C -A\sin2x\sin C = 4\sin2x+5\cos2x$
$\displaystyle \Rightarrow \left\{\begin{array}{l l}A\cos C = 5 & \quad\text{(1)}\\ A\sin C = -4&\quad\text{(2)}\end{array}\right.$
Square (1) and (2) and add:
$\displaystyle A^2 = 5^2+(-4)^2$
$\displaystyle \Rightarrow A = \sqrt{41}$
Divide (2) by (1):
$\displaystyle \tan C = -\tfrac45$
Grandad