Sine of Angle plus Straight Angle

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Theorem

$\map \sin {x + \pi} = -\sin x$


Proof

\(\ds \map \sin {x + \pi}\) \(=\) \(\ds \sin x \cos \pi + \cos x \sin \pi\) Sine of Sum
\(\ds \) \(=\) \(\ds \sin x \cdot \paren {-1} + \cos x \cdot 0\) Cosine of Straight Angle and Sine of Straight Angle
\(\ds \) \(=\) \(\ds -\sin x\)

$\blacksquare$


Also see


Sources

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