How do you find the exact value of sin (5pi)/3?

Sep 25, 2015

0 for $\sin \frac{5 \pi}{3}$ and $- \frac{\sqrt{3}}{2}$ for sin((5π)/3)

Explanation:

$\sin \frac{5 \pi}{3} = \frac{0}{3} = 0$

as $\sin \left(k \pi\right) = 0$ for all integer values of k

For sin((5π)/3),

sin((5π)/3)=sin((6π-π)/3)
=sin(2π-π/3)
=-sin(π/3)
$= - \frac{\sqrt{3}}{2}$