The terminal side of $\displaystyle-{{80}}^{\circ}\usepackage{cmbright}\Huge\$ lies in Quadrant IV where x is positive and y is negative, so $\displaystyle{\cos{\theta}}={x}\usepackage{cmbright}\Huge\$ is positive and $\displaystyle{\tan{\theta}}=\frac{{y}}{{x}}=\frac{{{\left(-\right)}}}{{{\left(+\right)}}}={\left(-\right)}\usepackage{cmbright}\Huge\$ is negative.