Answer
$\frac{24}{25}$
Work Step by Step
Given that $\sin A =\frac{-3}{5}$ and A is in quadrant 3
In Quadrant 3; $\cos A $ is negative.
$\cos A $ = -$\sqrt {1-\sin^{2}A}$
$\cos A $ = -$\sqrt {1-(\frac{3}{5})^{2}}$
$\cos A $ = -$\sqrt {1-(\frac{9}{25}}$
$\cos A $ = -$\sqrt {\frac{16}{25}}$
$\cos A $ = -$\frac{4}{5}$
$\sin 2A$ = 2 $\sin A \cos A$
Plug in $\sin A $ and $ \cos A $ values in above equation we get
$\sin 2A$ = $2 \times\frac{-3}{5}\times\frac{-4}{5}$
$\sin 2A$ = $\frac{24}{25}$
