Question

Find the value of the following trigonometric ratio :

\[ \sin \frac{17\pi}{6} \]

Solution

\[ \sin \frac{17\pi}{6} = \sin\left(2\pi+\frac{5\pi}{6}\right) \]

Using,

\[ \sin(2\pi+\theta)=\sin\theta \]

\[ = \sin\frac{5\pi}{6} \]

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

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

Answer :

\[ \boxed{ \sin\frac{17\pi}{6}=\frac{1}{2} } \]