# Find sin 2theta if theta is in the first quadrant and tan theta = 40/9 ??

Jul 18, 2018

$\frac{720}{1681}$.

#### Explanation:

Using the Identity, $\sin 2 \theta = \frac{2 \tan \theta}{1 + {\tan}^{2} \theta}$, we get,

$\sin 2 \theta = \frac{2 \cdot \frac{40}{9}}{1 + {\left(\frac{40}{9}\right)}^{2}}$,

$= \frac{80}{9} \div \frac{1681}{81}$.

$\Rightarrow \sin 2 \theta = \frac{720}{1681}$.

$\theta \in {Q}_{1} \Rightarrow 0 < \theta < \frac{\pi}{2} \Rightarrow 0 < 2 \theta < \pi$.

$\therefore \sin 2 \theta > 0$.