# Cosecant of Right Angle

## Theorem

$\csc 90^\circ = \csc \dfrac \pi 2 = 1$

where $\csc$ denotes cosecant.

## Proof

 $\displaystyle \csc 90^\circ$ $=$ $\displaystyle \frac 1 {\sin 90^\circ}$ Cosecant is Reciprocal of Sine $\displaystyle$ $=$ $\displaystyle \frac 1 1$ Sine of 90 Degrees $\displaystyle$ $=$ $\displaystyle 1$

$\blacksquare$