Answer
$0$
Work Step by Step
Need to solve $\sin [ n \times 180^{\circ} ] $
In order to solve the given expression we can use Trigonometric table of angles.
We know that $\sin (-\theta) =- \sin \theta$ and $\cos (-\theta) =\cos \theta$
Set $n=0, 1,2,3, .....$
Now, $\sin [ 0 \times 180^{\circ} ] =\sin 0^{\circ} =0$
$\sin [ 1 \times 180^{\circ} ] =\sin 180^{\circ} =0$
$\sin [ 2 \times 180^{\circ} ] =\sin 360^{\circ} =\sin 0$
Therefore, we can see that by substituting the different values of $n$ $\sin [ n \times 180^{\circ} ]=0$
