# Chapter 2 - Review Exercises - Page 94: 25

-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, $\frac{1}{\cos 222.5}\approx-1.3563417$.

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