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Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions1 Mark
Question
Write the value of $\sin10^\circ+\sin20^\circ+\sin30^\circ+...+\sin360^\circ.$
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Answer

$\sin(360^\circ-\theta)=-\sin\theta$
$\sin10^\circ+\sin20^\circ+...+\sin360^\circ$
$=\sin(360^\circ=350^\circ)+\sin(360^\circ-340^\circ)+\ ...\ \\\ +\sin180^\circ+\sin190^\circ+\ ...\ +\sin360^\circ$
$=-\sin350^\circ-\sin340^\circ-\ ...\ =\sin190^\circ\\\ \ \ \ +\sin180^\circ+\sin190^\circ+\ ...\ +\sin360^\circ$
$=\sin180^\circ+\sin360^\circ$
$=0+0$
$=0$

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