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

Key Concepts

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').