Question

$\sin 10^{\circ }+\sin 20^{\circ }+\sin 30^{\circ }+\dots \dots +\sin 360^{\circ }$ is equal to

Answer 1

Answer: 0

Given:
$\sin 10^{\circ }+\sin 20^{\circ }+\sin 30^{\circ }+\dots +\sin 270^{\circ }+\sin 360^{\circ }$
$\because \sin 190^{\circ }=\sin \left(180^{\circ }+10^{\circ }\right)=-\sin 10^{\circ }$
$\sin 200^{\circ }=-\sin 20^{\circ }$
$\sin 210^{\circ }=-\sin 30^{\circ }$
$\sin 360^{\circ }=\sin 180^{\circ }=0$
$\therefore$ Given expression is equal to zero.