Use a calculator to approximate the value of each expression. Give answers to six decimal places.sec 222° 30'

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Convert the angle from degrees and minutes to decimal degrees. Since there are 60 minutes in a degree, 30 minutes is 0.5 degrees. Therefore, 222° 30' becomes 222.5°.

Recall that the secant function is the reciprocal of the cosine function. Therefore, \( \sec(\theta) = \frac{1}{\cos(\theta)} \).

Use a calculator to find \( \cos(222.5°) \).

Calculate the reciprocal of the cosine value obtained in the previous step to find \( \sec(222.5°) \).

Round the result to six decimal places as required.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Secant Function

The secant function, denoted as sec(θ), is the reciprocal of the cosine function. It is defined as sec(θ) = 1/cos(θ). Understanding this relationship is crucial for calculating secant values, especially when dealing with angles expressed in degrees and minutes.

Angle Conversion

In trigonometry, angles can be expressed in degrees, minutes, and seconds. To accurately compute trigonometric functions, it is often necessary to convert these angles into decimal degrees. For example, 222° 30' can be converted to decimal form by calculating 222 + (30/60) = 222.5°.

Calculator Functions

Using a scientific calculator effectively is essential for evaluating trigonometric functions. Students must ensure that the calculator is set to the correct mode (degrees or radians) corresponding to the angle being used. This ensures accurate results when calculating values like sec(222° 30').