# Thread: high school trig hmwk question, desperate help needed =[

1. ## high school trig hmwk question, desperate help needed =[

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

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

4. 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
$\displaystyle sin(2 \theta) = 2~sin(\theta)~cos(\theta)$

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

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

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

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

-Dan

5. Originally Posted by topsquark
$\displaystyle = 2~tan(\theta)~cos^2(\theta)$
Sure. Now from $\displaystyle \frac{1} {{\cos ^2 \theta }} = 1 + \tan ^2 \theta \implies \cos ^2 \theta = \frac{1} {{1 + \tan ^2 \theta }}.$

So $\displaystyle \sin 2\theta = \frac{{2\tan \theta }} {{1 + \tan ^2 \theta }}.$

I think he means that.

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Ohhh, nice formula, could be helpful to integrate someday