Answer
$\displaystyle \frac{5}{4}$
Work Step by Step
We don't have a tabular angle for which $\displaystyle \cos t=\frac{3}{5}$, so we construct a right triangle in which this trigonometric ratio (adjacent/hypotenuse) equals $\displaystyle \frac{3}{5}$. See image below.
$t=\displaystyle \arccos\frac{3}{5}$
Using the Pythagorean theorem, $\left[\begin{array}{l}
b^{2}+3^{2}==5^{2}\\
b=\sqrt{25-9}\\
b=4
\end{array}\right]$
$\displaystyle \csc(\arccos\frac{3}{5})=\csc t=\frac{hyp.}{opp.}=\frac{5}{4}$
