Question

Write the value of $\sin {10}^o+\sin {20}^o+\sin {30}^o+...+\sin {360}^o$

Answer 1

answer is zero.

= sin 10+sin20+sin30 + sin40 +...sin180 + sin(360-170)+ ……...+sin(360-40)+sin(360-30)+sin(360-20)+sin360-10)+sin360

sin360-x = - sin x

here all the terms cancled out

so, sin10+sin20+sin30+....+sin360=0