Refer to the $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle. The side opposite $\displaystyle{{30}}^{\circ}\usepackage{cmbright}\Huge\$ has length 1 and the hypotenuse has length 2, so:

$\displaystyle{{\sin{{30}}}}^{\circ}=\frac{{o}}{{h}}=\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$

Cosecant is the reciprocal of sine, so:

$\displaystyle{{\csc{{30}}}}^{\circ}=\frac{{1}}{{\frac{{1}}{{2}}}}={2}\usepackage{cmbright}\Huge\$