Question

Find the value of the following trigonometric ratio :

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

Solution

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

Using,

\[ \sin(-\theta)=-\sin\theta \]

\[ = -\sin\left(2\pi-\frac{\pi}{6}\right) \]

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

\[ = \frac{1}{2} \]

Answer :

\[ \boxed{ \sin\left(-\frac{11\pi}{6}\right)=\frac{1}{2} } \]