Question

Find the values of the following trigonometric ratio:

\[\sin\frac{151\pi}{6}\]

Answer 1

We have: 
\[\sin\frac{151\pi}{6} = \sin 4530^\circ\]
\[4530^\circ = 90^\circ \times 50 + 30^\circ\]
\[4530^\circ\text{ lies in the third quadrant in which the sine function is negative . }\]
Also, 50 is an even integer .
\[ \therefore \sin \left( 4530^\circ \right) = \sin \left( 90^\circ \times 50 + 30^\circ \right) = - \sin \left( 30^\circ \right) = - \frac{1}{2}\]