Weird basic question

**Punch** · January 28th 2010, 03:04 AM

$<br /> sin(x+50)=2cosx<br />$

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!!

**CaptainBlack** · January 28th 2010, 03:23 AM

Originally Posted by Punch

$<br /> sin(x+50)=2cosx<br />$

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

**Punch** · January 28th 2010, 03:26 AM

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?

**CaptainBlack** · January 28th 2010, 03:28 AM

Originally Posted by Punch

Thanks but how do I solve for x with this?

arctan

CB

**Punch** · January 28th 2010, 03:29 AM

Originally Posted by CaptainBlack

arctan

CB

SOrry but what is arctan?

**HallsofIvy** · January 28th 2010, 04:03 AM

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 $\frac{1}{tan(x)}= cot(x)$ .

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