Answer
$\sec 590.9^{\circ}$ = - 1.5856
Work Step by Step
Using calculator in degree mode-
590.9 → $\cos$ → $\frac{1}{x}$ (Recall $\sec\theta$ = $\frac{1}{\cos\theta}$)
$\sec 590.9^{\circ}$ = - 1.5856006972
Rounding it to four places past the decimal point-
$\sec 590.9^{\circ}$ = - 1.5856