Use a calculator to find a decimal approximation for the following trigonometric function. \[ \sec 34^{\circ} 30^{\prime} \] \[ \sec 34^{\circ} 30^{\prime} \approx \] (Round to seven decimal places as needed.)

Step 1 ：Convert the given angle from degrees and minutes to decimal degrees. We have 34 degrees and 30 minutes. Since 1 degree is equal to 60 minutes, 30 minutes is equal to \(\frac{30}{60} = 0.5\) degrees. So, the total angle in decimal degrees is \(34 + 0.5 = 34.5\) degrees.

Step 2 ：Convert the angle from degrees to radians. The conversion factor is \(\frac{\pi}{180}\). So, \(34.5\) degrees is equal to \(34.5 \times \frac{\pi}{180} = 0.6021385919380436\) radians.

Step 3 ：Find the cosine of the angle. Using a calculator, we find that \(\cos(0.6021385919380436) = 0.8241261886220157\).

Step 4 ：Find the secant of the angle. The secant is the reciprocal of the cosine. So, \(\sec(34.5) = \frac{1}{\cos(34.5)} = \frac{1}{0.8241261886220157} = 1.2134064100936472\).

Step 5 ：Round the result to seven decimal places. The decimal approximation for the secant of \(34^\circ 30^\prime\) is \(1.2134064\).