Mathematics

Problem

Find exact values for

\sin \theta

and

\cos \theta

given that: a)

\tan \theta = \frac{2}{3}

and

0 < \theta < \frac{\pi}{2}

\tan \theta = -\frac{4}{3}

and

\frac{\pi}{2} < \theta < \pi

\tan \theta = \frac{\sqrt{5}}{3}

and

\pi < \theta < \frac{3\pi}{2}

\tan \theta = -\frac{12}{5}

and

\frac{3\pi}{2} < \theta < 2\pi