Question

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

• A. $1$
• B. $0$
• C. $-1$
• D. None of these

Answer 1

The correct option is B $0$

$\sin {10}^{\circ }+\sin {20}^{\circ }+\sin {30}^{\prime }+\dots +\sin {360}^{\circ }$

$(\sin 10+\sin 350)+(\sin 20+\sin 340)+\cdots +\sin {360}^{\circ }$

$(\sin 10+\sin (360-10\left)\right)+(\sin 20+\sin (360-20)$

$+\dots +\sin {360}^{\circ }$

$(\sin 10-\sin 10)+(\sin 20-\sin {20}^{\circ })+\cdots +\sin {360}^{\circ }$

$0+0+\cdots +0+0$

$=0$

option b is correct Answer.