Answer
$\csc 12.21^{\circ}$ =4.7282
Work Step by Step
Using calculator in degree mode-
$\csc 12.21^{\circ}$ =4.7282355708
(Finding $\sin$ first and then using reciprocal $\frac{1}{x}$)
Rounding it to four places past the decimal point-
$\csc 12.21^{\circ}$ =4.7282