Answer
$\csc$ 60$^{\circ}$ = $\frac{2\sqrt 3}{3}$
Work Step by Step
$\csc$ 60$^{\circ}$
We must find side $x$ of the 30$^{\circ}$ - 60$^{\circ}$ Right Triangle.
Pythagorean Theorem: $c$$^{2}$ = $a$$^{2}$ + $b$$^{2}$
2$^{2}$ = 1$^{2}$ + $x$$^{2}$
4 = 1 + $x$$^{2}$
x$^{2}$ = 3
x = $\sqrt 3$
Now consider the triangle from the perspective of the 60$^{\circ}$ angle.
Hypotenuse = 2
Opposite = $\sqrt 3$
Adjacent = 1
$\csc$ 60$^{\circ}$ = $\frac{Hypotenuse}{Opposite}$ = $\frac{2}{\sqrt 3}$ = $\frac{2\sqrt 3}{3}$
Therefore:
$\csc$ 60$^{\circ}$ = $\frac{2\sqrt 3}{3}$
