## Precalculus (6th Edition)

$\displaystyle \cos 2\theta=-\frac{19}{25}$ $\displaystyle \sin 2\theta=\frac{2\sqrt{66}}{25}$
Plan: work out $\sin\theta$, then apply the double-angle identities. Pythagorean Identity ($\sin\theta$ is positive): $\sin\theta=+\sqrt{1-\cos^{2}\theta}=\sqrt{1-\dfrac{3}{25}}$ $=\displaystyle \sqrt{\frac{22}{25}}=\frac{\sqrt{22}}{5}$ Double-Angle Identities: $\displaystyle \cos 2\theta=2\cos^{2}\theta-1=2(\frac{\sqrt{3}}{5})^{2}-1$ $=2\displaystyle \cdot\frac{3}{25}-1=\frac{6}{25}-1=-\frac{19}{25}$ $\sin 2\theta=2\sin\theta\cos\theta$ $=2(\displaystyle \frac{\sqrt{22}}{5})(\frac{\sqrt{3}}{5}$)$=\displaystyle \frac{2\sqrt{66}}{25}$