Answer
$sin2x=\frac{24}{25}$
$cos2x=\frac{7}{25}$
$tan2x=\frac{24}{7}$
Work Step by Step
Given $sin(x)=-\frac{3}{5}$ and $x$ in Quadrant III, we have $cos(x)=-\frac{4}{5}$ and $tan(x)=\frac{3}{4}$.
$sin2x=2sin(x)cos(x)=2\times(-\frac{3}{5})\times(-\frac{4}{5})=\frac{24}{25}$
$cos2x=2)cos^2(x)-1=2\times(-\frac{4}{5})^2-1=\frac{7}{25}$
$tan(2x)=\frac{sin2x}{cos2x}=\frac{24/25}{7/25}=\frac{24}{7}$
or $tan(2x)=\frac{2tan(x)}{1-tan^2x}=\frac{2\times3/4}{1-9/16}=\frac{24}{7}$
