# Cotangent of Angle plus Straight Angle

## 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

$\blacksquare$