Answer
$1.9362132$
Work Step by Step
Using the reciprocal identity $\sec\theta=\frac{1}{\cos\theta}$,
$\sec 58.9041^{\circ}=\frac{1}{\cos 58.9041^{\circ}}$
Ensuring that the calculator is in degree mode, we type $\frac{1}{\cos 58.9041}$ into the calculator and solve:
$\frac{1}{\cos 58.9041^{\circ}}\approx1.9362132$