First slide

Trigonometric Identities

Question

The value of $\sin 10^{\circ} + \sin 20^{\circ} + \sin 30^{\circ} + \dots + \sin 360^{\circ}$ , is

Easy

A

1
B

0
C

$- 1$
D

$1 / 2$

Solution

We have, $\sin (π + θ) = - \sin θ$
$\begin{aligned} ∴ \sin 190^{\circ} = - \sin 10^{\circ}, \sin 200^{\circ} = - \sin 20^{\circ}, \\ \sin 210^{\circ} = - \sin 30^{\circ}, \sin 360^{\circ} = \sin 180^{\circ} = 0 \end{aligned}$
Thus, all the terms in the given series cancel with each other. Consequently, the sum is zero.

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