Answer
- $\frac{2\sqrt 3}{3}$
Work Step by Step
To find exact value of $\csc 300^{\circ}$, let's find its reference angle first. As $ 300^{\circ}$ terminates in quadrant IV,
The reference angle = $ 360^{\circ} - 300^{\circ}$ = $60^{\circ}$
As $ 300^{\circ}$ terminates in quadrant IV, its $\csc$ will be negative. Therefore by reference angle theorem-
$\csc 300^{\circ}$ = - $\csc 60^{\circ}$
= - $\frac{2}{\sqrt 3}$ = - $\frac{2\sqrt 3}{3}$