The terminal side of $\displaystyle-{{190}}^{\circ}\usepackage{cmbright}\Huge\$ lies in Quadrant II. Since $\displaystyle{\sin{\theta}}={y}\usepackage{cmbright}\Huge\$ and y is positive in Quadrant II, $\displaystyle{\sin{\theta}}\usepackage{cmbright}\Huge\$ is positive. Since cosecant is the reciprocal of sine, it is also positive.