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Question
Write the value of sin 10° + sin 20° + sin 30° + ... + sin 360°.
Solution
\[ = \sin10^\circ + \sin20^\circ + . . . + \sin180^\circ - \sin170^\circ - \sin160^\circ - . . . - \sin20^\circ - \sin10^\circ + \sin360^\circ \left( \because \sin\left( 360^\circ - x \right) = - \sin x \right)\]
\[ = \sin180^\circ + \sin360^\circ\]
\[ = 0 + 0\]
\[ = 0\]
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