Question

The Value of Sin10+Sin20+Sin30+...............Sin360 is

Answer 1

Answer: Zero

Solution:

i) There are 36 terms;

ii) Group them as: (sin10° + sin350°) + (sin20° + sin340°) + (sin30° + sin330°) + ....

+ .. + (sin170° + sin190°) + (sin180° + sin360°)

This forms to 18 pairs.

Each pair is zero.

sin10° + sin350° = sin10° + sin(360 - 10) = sin10° - sin10° = 0

Like this every pair becomes zero.

Thus total sum is zero.