## Trigonometry (11th Edition) Clone

$tan(2\theta) = \frac{24}{7}$
If $90^{\circ} \lt \theta \lt 180^{\circ}$, then the angle $\theta$ is in quadrant II. If the hypotenuse is 5, and the adjacent side has a length of 3, then the length of the opposite side is $\sqrt{5^2-3^2} = 4$ From part (a), we know that $cos(2\theta) = -\frac{7}{25}$ From part (b), we know that $sin(2\theta) = -\frac{24}{25}$ We can find $tan(2\theta)$: $tan(2\theta) = \frac{sin(2\theta)}{cos(2\theta)}$ $tan(2\theta) = \frac{-\frac{24}{25}}{-\frac{7}{25}}$ $tan(2\theta) = \frac{24}{7}$