# Math Help - sin a sinx+ b cosx

1. ## sin a sinx+ b cosx

Hey.
The question is find the value of R and the value of A.

sinx+ 2cosx = Rcos(x-A)

i can find R which is square root of 5, but i keep getting 1.11 for A and the answer is 0,46 (radians)

can anyone help?

2. Hello Oasis1993
Originally Posted by Oasis1993
Hey.
The question is find the value of R and the value of A.

sinx+ 2cosx = Rcos(x-A)

i can find R which is square root of 5, but i keep getting 1.11 for A and the answer is 0,46 (radians)

can anyone help?
$R\cos(x-A) = R\cos x \cos A + R \sin x \sin A=\sin x + 2\cos x$

$\Rightarrow R\sin A = 1,\;R\cos A = 2$

$\Rightarrow \tan A =\tfrac12$

$\Rightarrow A = 0.46...$