Since \(\displaystyle \L\\sin({\theta})=\frac{5}{8}\), use the identities:
\(\displaystyle \L\\cos(2{\theta})=1-2sin^{2}({\theta})\)
and
\(\displaystyle \L\\sin(2{\theta})=2sin({\theta})cos({\theta})\)
If \(\displaystyle \L\\sin(5/8)\), then \(\displaystyle \L\\cos({\theta})=\frac{\sqrt{39}}{8}\)
