Answer
$37.695528^{\circ}$
Work Step by Step
Step 1: Using the reciprocal identity $\sec\theta=\frac{1}{\cos\theta}$, we write $\sec \theta=1.2637891$ as $\frac{1}{\cos\theta}=1.2637891$
Step 2: Using cross-multiplication,
$\frac{1}{\cos\theta}=\frac{1.2637891}{1}$ is written as $\cos\theta=\frac{1}{1.2637891}$
Step 3: Writing $\cos\theta=\frac{1}{1.2637891}$ as $\theta=\cos^{-1} \frac{1}{1.2637891}$
Step 4: Using degree mode, we type $\cos^{-1} \frac{1}{1.2637891}$ into the calculator and solve:
$\theta=\cos^{-1} \frac{1}{1.2637891}=37.695528^{\circ}$
