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
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
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