Question

Find tan(x) in terms of sin^2(x), could be in any quadrant

Answer 1

\[
\tan(x) = \frac{\sin(x)}{\cos(x)} = \frac{\sqrt{\sin^2(x)}}{\sqrt{\cos^2(x)}} = \frac{\sqrt{\sin^2(x)}}{\sqrt{1-\sin^2(x)}}
\]Well sort of... it really is \(|\sin(x)|=\sqrt{\sin^2(x)}\) so we have to account for sign change some how.