Question

Find the value of $\sin 2\theta$ if $\sin \theta =\frac{-3}{5}$ and $\pi <\theta <3\frac{\pi }{2}$

Answer 1

Given that $\theta$ lies in $Q_3$

So, $2\pi <\theta <3\pi$

Given that $\sin \theta =\frac{-3}{5}$

Therefore, $\cos \theta =\frac{4}{5}$

$\Rightarrow \sin 2\theta =2\sin \theta \cos \theta$

$\Rightarrow \sin 2\theta =2\left(\frac{-3}{5}\right)\left(\frac{-4}{5}\right)$

$\Rightarrow \sin 2\theta =\frac{24}{25}$