# Question #0c74b

May 7, 2017

$\sin \left({9480}^{\circ}\right) = \sin \left({120}^{\circ}\right) = \frac{\sqrt{3}}{2}$

#### Explanation:

(I have assumed you have wrote the angle in degrees rather than radians although there isn't a degree symbol)
We can first start by simplifying the expression inside the sine function:
$\sin \left({90}^{\circ} \cdot {105}^{\circ} + {30}^{\circ}\right) = \sin \left({9450}^{\circ} + {30}^{\circ}\right) = \sin \left({9480}^{\circ}\right)$
Here we must find the reference angle of ${9480}^{\circ}$:
Since ${360}^{\circ}$ is one full circle around the unit circle, we can do:
$9480 \mod 360 = 120$ to find the remainder when 9480 is divided by 360.
Therefore $\sin \left({9480}^{\circ}\right) = \sin \left({120}^{\circ}\right) = \frac{\sqrt{3}}{2}$