Answer
-1.3563417
Work Step by Step
Step 1: First, we convert the angle in decimal degrees:
$222^{\circ}30'=222\frac{30}{60}^{\circ}=222.5^{\circ}$
Therefore, $\sec 222^{\circ}30'=\sec 222.5^{\circ}$.
Step 2: Using the reciprocal identity $\sec\theta=\frac{1}{\cos\theta}$,
$\sec 222.5=\frac{1}{\cos 222.5}$
Step 3: Now, we check to ensure that the calculator is in degree mode.
Step 4: We then type $\frac{1}{\cos 222.5}$ into the calculator.
Step 5: Solving, $\frac{1}{\cos 222.5}\approx-1.3563417$.
