Refer to the $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle. The side opposite $\displaystyle{{60}}^{\circ}\usepackage{cmbright}\Huge\$ has length $\displaystyle\sqrt{{3}}\usepackage{cmbright}\Huge\$ and the hypotenuse has length 2, so:

$\displaystyle{{\sin{{60}}}}^{\circ}=\frac{{o}}{{h}}=\frac{\sqrt{{3}}}{{2}}\usepackage{cmbright}\Huge\$

Cosecant is the reciprocal of sine, so:

$\displaystyle{{\csc{{60}}}}^{\circ}=\frac{{1}}{{\frac{\sqrt{{3}}}{{2}}}}=\frac{{2}}{\sqrt{{3}}}\usepackage{cmbright}\Huge\$