# How do you find the exact value of sin690?

Jul 26, 2018

$- \frac{1}{2}$.

#### Explanation:

$\sin {690}^{\circ} = \sin \left({720}^{\circ} - {30}^{\circ}\right)$,

$= \sin \left(4 \pi - \frac{\pi}{6}\right)$.

But, $\sin \left(4 \pi - \theta\right) = - \sin \theta$.

$\therefore \sin {690}^{\circ} = - \sin {30}^{\circ} = - \frac{1}{2}$.