Question

Find the value of the following trigonometric ratio:

\[\sin\frac{5\pi}{3}\]

Answer 1

 We have: 
\[\frac{5\pi}{3} = \left( \frac{5}{3} \times 180 \right)^\circ = 300^\circ = \left( 90^\circ \times 3 + 30^\circ \right)\]
\[300^\circ\text{ lies in the fourth quadrant in which the sine function is negative . }\]
Also, 3 is an odd integer . 
\[ \therefore \sin\left( \frac{5\pi}{3} \right) = \sin \left( 300^\circ \right) = \sin \left( 90^\circ \times 3 + 30^\circ \right) = - \cos30^\circ = - \frac{\sqrt{3}}{2}\]