Find the indicated function value. If it is undefined, say so. See Example 4. sec 1800°

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 the secant function is crucial for evaluating secant values at specific angles, as it directly relates to the cosine function's behavior.

Angle Measurement

Angles can be measured in degrees or radians. In this question, 1800° is an angle measured in degrees. To evaluate trigonometric functions, it is often necessary to convert large angles into a standard position by subtracting multiples of 360° (for degrees) or 2π (for radians) to find an equivalent angle within the range of 0° to 360°.

Undefined Values in Trigonometry

Certain trigonometric functions can be undefined for specific angles. For example, sec(θ) is undefined when cos(θ) = 0. Recognizing when a function is undefined is essential for accurately determining function values and understanding the behavior of trigonometric functions at critical points.