The terminal side of $\displaystyle-{{80}}^{\circ}\usepackage{cmbright}\Huge\$ lies in Quadrant IV. Since $\displaystyle{\cos{\theta}}={x}\usepackage{cmbright}\Huge\$ and x is positive in Quadrant IV, $\displaystyle{\cos{\theta}}\usepackage{cmbright}\Huge\$ is positive. Since secant is the reciprocal of cosine, it is also positive.