high school trig hmwk question, desperate help needed =[

**Morinphen** · November 30th 2007, 06:39 AM

Hello, here is the question:

express sin2(theta) and cos2(theta) in terms of tan(theta). We have only learned compound and double angles so far, so I assume we are supposed to work with those, help is greatly appreciated =S

**jabroni1212** · November 30th 2007, 06:49 AM

do you mean $cos^2(\theta)$ or $cos(2\theta)$ ??

**Morinphen** · November 30th 2007, 07:34 AM

, sry about that

**topsquark** · November 30th 2007, 09:16 AM

Originally Posted by Morinphen

Hello, here is the question:

express sin2(theta) and cos2(theta) in terms of tan(theta). We have only learned compound and double angles so far, so I assume we are supposed to work with those, help is greatly appreciated =S

$sin(2 \theta) = 2~sin(\theta)~cos(\theta)$

$= 2~sin(\theta)~cos(\theta) \cdot \frac{cos(\theta)}{cos(\theta)}$

$= 2 \frac{sin(\theta)}{cos(\theta)}cos^2(\theta)$

$= 2~tan(\theta)~cos^2(\theta)$

Something like that? If you have an example of what your instructor is looking for it would be helpful.

-Dan

**Krizalid** · November 30th 2007, 09:52 AM

Originally Posted by topsquark

$= 2~tan(\theta)~cos^2(\theta)$

Sure. Now from $\frac{1}<br /> {{\cos ^2 \theta }} = 1 + \tan ^2 \theta \implies \cos ^2 \theta = \frac{1}<br /> {{1 + \tan ^2 \theta }}.$

So $\sin 2\theta = \frac{{2\tan \theta }}<br /> {{1 + \tan ^2 \theta }}.$

I think he means that.

--

Ohhh, nice formula, could be helpful to integrate someday

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