Given:
[tex]\sin \theta=\frac{3\sqrt[]{2}}{5}[/tex][tex]\begin{gathered} \sin 2\theta=2\sin \theta\cos \theta \\ \sin 2(\frac{\theta}{2})=2\sin (\frac{\theta}{2})\cos (\frac{\theta}{2}) \\ \sin \theta=2\sin (\frac{\theta}{2})\cos (\frac{\theta}{2}) \\ \frac{3\sqrt[]{2}}{5\times2}=\sin (\frac{\theta}{2})\cos (\frac{\theta}{2}) \end{gathered}[/tex][tex]\begin{gathered} \cos ^2\theta=1-\sin ^2\theta \\ \cos ^2\theta=1-(\frac{3\sqrt[]{2}}{5})^2 \\ \cos ^2\theta=1-\frac{18}{25} \\ \cos ^2\theta=\frac{7}{25} \end{gathered}[/tex][tex]\cos \theta=\frac{\sqrt[]{7}}{5}[/tex]
