Question

Find the approximate value of sin$\left(\frac{5\pi }{16}\right).$

Answer 1

$\sin \left(\frac{5\pi }{16}\right)$

$=\cos (\frac{\pi }{2}-\frac{5\pi }{16})$ since $\sin \theta =\cos (\frac{\pi }{2}-\theta )$

$=\cos \left(\frac{8\pi -5\pi }{16}\right)$

$=\cos \left(\frac{3\pi }{16}\right)$

$=\cos \frac{3\times 180}{16}$

$=\cos \frac{3\times 45}{4}$

$=\cos \frac{135}{4}$

$=\cos 33.75‬$

$=-0.69129$