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How can be deduced the so called "small angle approximations" for sine, cosine and tangent, namely

$\sin \theta \approx \theta$

$\tan\theta \approx \theta$

$\cos\theta \approx 1-\frac{\theta^2}{2}$

By means of any geometric construction? Of course, here $\theta$ is in radians. How to prove these approximations by means of geometry?

Espantosidad
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    You should probably look at http://math.stackexchange.com/questions/75130/how-to-prove-that-lim-limits-x-to0-frac-sin-xx-1 – digital-Ink Jun 05 '16 at 20:55

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