# Cosecant of Angle plus Straight Angle

## Theorem

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

## Proof

 $\ds \map \csc {x + \pi}$ $=$ $\ds \frac 1 {\map \sin {x + \pi} }$ Cosecant is Reciprocal of Sine $\ds$ $=$ $\ds \frac 1 {-\sin x}$ Sine of Angle plus Straight Angle $\ds$ $=$ $\ds -\csc x$ Cosecant is Reciprocal of Sine

$\blacksquare$