Question

The value of the $\sin 1^{\circ }+\sin 2^{\circ }+......+\sin 359^{\circ }$ is equal to

• A. 0
• B. 1
• C. -1
• D. $180$

Answer 1

Answer: (A)

$\sin 1^{\circ }+\sin 2^{\circ }+\sin 3^{\circ }+\dots +\sin 359^{\circ }$
$=\left(\sin 1^{\circ }+\sin 359^{\circ }\right)+\left(\sin 2^{\circ }+\sin 358^{\circ }\right)+\dots +\sin 180^{\circ }$
$=0+0+0+\dots +0=0$
$\left[\because \sin \theta +\sin \left(360^{\circ }-\theta \right)=0\right]$