Cotangent of Angle plus Straight Angle

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Theorem

$\map \cot {x + \pi} = \cot x$


Proof

\(\ds \map \cot {x + \pi}\) \(=\) \(\ds \frac {\map \cos {x + \pi} } {\map \sin {x + \pi} }\) Cotangent is Cosine divided by Sine
\(\ds \) \(=\) \(\ds \frac {-\cos x} {-\sin x}\) Cosine of Angle plus Straight Angle and Sine of Angle plus Straight Angle
\(\ds \) \(=\) \(\ds \cot x\) Cotangent is Cosine divided by Sine

$\blacksquare$


Also see


Sources

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