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What is the value of sin 0° + sin 10° + sin 20° + sin 30° + ⋯ + sin 360°?

What is the value of sin 0° + sin 10° + sin 20° + sin 30° + ⋯ + sin 360°? Correct Answer 0

Formula used:

sin(360° - θ) = - sin θ  

Calculation:

sin 0° + sin 10° + sin 20° + sin 30° + ⋯ + sin 360°

⇒ sin 0° + sin 10° + ....+ sin 180° + sin (360 - 170°) +  sin (360 - 160°) + .....+ sin (360 - 10°) + sin (360 - 0°)  

By using the  above formula

⇒ sin 0° + sin 10° + ......- sin 10° - sin 0° = 0

∴ sin 0° + sin 10° + sin 20° + sin 30° + ⋯ + sin 360° = 0

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