# Thread: Weird basic question

1. ## Weird basic question

$
sin(x+50)=2cosx
$

It's weird that this question doesn't have any special angle or any sort, I don't know how to solve this question with $50^\circ$ as the angle!!

2. Originally Posted by Punch
$
sin(x+50)=2cosx
$

It's weird that this question doesn't have any special angle or any sort, I don't know how to solve this question with $50^\circ$ as the angle!!
$\sin(x+50)=\sin(x)\cos(50)+\cos(x)\sin(50)=2\cos(x )$

so:

$\tan(x)=\frac{2-\sin(50)}{\cos(50)}$

CB

3. Originally Posted by CaptainBlack
$\sin(x+50)=\sin(x)\cos(50)+\cos(x)\sin(50)=2\cos(x )$

so:

$\tan(x)=\frac{2-\sin(50)}{\cos(50)}$

CB
Thanks but how do I solve for x with this? Also, how did you relate tan(x) with this?

4. Originally Posted by Punch
Thanks but how do I solve for x with this?
arctan

CB

5. Originally Posted by CaptainBlack
arctan

CB
SOrry but what is arctan?

6. It is the inverse function to tangent. tan(arctan(x))= x and arctan(tan(x))= x as long as x is between $-pi/2$ and $\pi/2$. Also called $tan^{-1}(x)$ which must not be confused with $\frac{1}{tan(x)}= cot(x)$.