Answer
$cot(arcsin~\frac{3}{8})=\frac{\sqrt {55}}{3}$
Work Step by Step
$y=arcsin~\frac{3}{8}$
$sin~y=\frac{3}{8},~~$ (Notice that $0°\lt y\lt90°$)
$cos^2y+sin^2y=1$
$cos^2y=1-\frac{9}{64}=\frac{55}{64}$
$cos~y=\frac{\sqrt {55}}{8}$
$cot(arcsin~\frac{3}{8})=cot~y=\frac{cos~y}{sin~y}=\frac{\sqrt {55}}{3}$
