Answer
1.021034
Work Step by Step
$78^{\circ}21'=78^{\circ}+\frac{21}{60}^{\circ}=78^{\circ}+0.35^{\circ}=78.35^{\circ}$
$\csc 78^{\circ}21'=\csc 78.35^{\circ}=\frac{1}{\sin 78.35^{\circ}}$
Using a calculator in degree mode, we can find
$\frac{1}{\sin 78.35^{\circ}}\approx1.021034$
