What is $cos^theta$ in terms of $sintheta$ ?

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Answer 1 · 2015-12-18T00:14:58

If $theta$ is in Q1 or Q4 then $cos theta = sqrt(1-sin^2 theta)$

If $theta$ is in Q2 or Q3 then $cos theta = -sqrt(1-sin^2 theta)$

We always have $cos^2 theta + sin^2 theta = 1$ regardless of which quadrant $theta$ is in. Hence we always have:

$cos theta = +-sqrt(1-sin^2 theta)$

If $theta$ is in Q1 or Q4 then $cos theta >= 0$ , hence:

$cos theta = sqrt(1-sin^2 theta)$

If $theta$ is in Q2 or Q3 then $cos theta <= 0$ , hence:

$cos theta = -sqrt(1-sin^2 theta)$

What is cos^thetacos^theta in terms of sinthetasintheta?