Question

Find the value of the following trigonometric ratio :

\[ \sin\left(\frac{151\pi}{6}\right) \]

Solution

\[ \sin\left(\frac{151\pi}{6}\right) = \sin\left(\frac{151\pi}{6}-24\pi\right) \]

\[ = \sin\frac{7\pi}{6} \]

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

Using,

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

\[ = -\sin\frac{\pi}{6} = -\frac{1}{2} \]

Answer :

\[ \boxed{ \sin\left(\frac{151\pi}{6}\right) = -\frac{1}{2} } \]