Answer
$\sec 311.7^{\circ}$ = 1.5032
Work Step by Step
Using calculator in degree mode-
311.7 → $\cos$ → $\frac{1}{x}$ (Recall $\sec\theta$ = $\frac{1}{\cos\theta}$)
$\sec 311.7^{\circ}$ = 1.5032386797
Rounding it to four places past the decimal point-
$\sec 311.7^{\circ}$ = 1.5032