Question

Find the values of the following trigonometric ratio:

\[\sin\left( - \frac{11\pi}{6} \right)\]

 

Answer 1

We have:
\[\sin\left( - \frac{11\pi}{6} \right) = \sin \left( - 330^\circ \right)\]
\[\sin \left( - 330^\circ \right) = - \sin \left( 330^\circ \right) = - \sin \left( 90^\circ \times 3 + 60^\circ \right)\]
\[330^\circ\text{ lies in the fourth quadrant in which the sine function is negative .} \]
Also, 3 is an odd integer . 
\[ \therefore \sin\left( - 330^\circ \right) = - \sin\left( 330^\circ \right) = - \sin\left( 90^\circ \times 3 + 60^\circ \right) = - \left( - \cos60^\circ \right) = - \left( - \frac{1}{2} \right) = \frac{1}{2}\]