What is the value of sin 10° + sin 20° + sin 30° + ... + sin 360°

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Solution

sin 10° + sin 20° + sin 30° + ... + sin 360°
sin 10° + sin 20° + sin 30° + ...+sin340°+sin 350° + sin 360°
sin 10° + sin 20° + sin 30° + ... + sin(360-20)+sin (360°-10°)+ sin360°
sin10°-sin10° + sin20°- sin-20° + sin30°- sin30° + ....... sin360° [ since sin (360 -x) = -sinx]
0 + 0 + 0 .......+0 +0 +0
= 0

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sin 10^{\circ} + sin 20^{\circ} + sin 30^{\circ} + . . . . + sin 360^{\circ}

sin10°+sin20°+sin30°+....+sin360°=?

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