If A lies between $270°$ and $360°$ and $\sin A=-\frac{7}{25}$ , then

Given $270<A<360$

$\Rightarrow \sin A=-\frac{7}{25}$

$\Rightarrow \cos A=\frac{24}{25}$

$\Rightarrow \sin \frac{A}{2}=\sqrt{\frac{1-\cos A}{2}}$

$=\sqrt{\frac{1-\frac{24}{25}}{2}}$

$\Rightarrow \sin \frac{A}{2}=\sqrt{\frac{1}{50}}$

$=\sqrt{\frac{2}{100}}$

$\Rightarrow \sin \frac{A}{2}=\frac{\sqrt{2}}{10}$

$\Rightarrow \cos \frac{A}{2}=\sqrt[-1]{\frac{1+\cos A}{2}}\left[\because 135<\frac{A}{2}<180,\frac{A}{2}\in {\theta }_2\right]$

$=\sqrt[-]{\frac{25+24}{50}}$

$=\sqrt[-]{\frac{49}{50}}$

$\Rightarrow \cos \frac{A}{2}=-\frac{7\sqrt{2}}{10}$

$\Rightarrow \tan \frac{A}{2}=\frac{\sin \frac{A}{2}}{\cos \frac{A}{2}}$

$=\frac{\sqrt{2}}{10}\times \frac{10}{-7\sqrt{2}}=-\frac{1}{7}$

$\Rightarrow \sin 2A=2\sin A.\cos A$

$=2\times \frac{-7}{25}\times \frac{24}{25}=\frac{-336}{225}$