Answer
$\csc 670^{\circ} 20'$ = -1.3118
Work Step by Step
Given function-
$\csc 670^{\circ} 20'$
We have to convert it to decimal degrees first-
$\csc 670^{\circ} 20'$= $\csc (670^{\circ} + 20')$
= $\csc (670^{\circ} + (\frac{20}{60})^{\circ})$
= $\csc (670^{\circ} + (0.3333)^{\circ})$
= $\csc 670.3333^{\circ} $
Using calculator in degree mode-
670.3333 → $\sin$ → $\frac{1}{x}$ (Recall $\csc\theta$ = $\frac{1}{\sin\theta}$)
$\csc 670.3333^{\circ}$ = -1.3118327614
Rounding it to four places past the decimal point-
$\csc 670.3333^{\circ}$ = -1.3118
or
$\csc 670^{\circ} 20'$ = -1.3118
