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

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

Convert the angle from degrees to a standard position by finding its equivalent angle between 0° and 360°. This can be done by finding the remainder when 1800° is divided by 360°.

Calculate 1800° modulo 360° to find the equivalent angle. This will help in determining the cosine of the angle.

Once the equivalent angle is found, determine \( \cos(\theta) \) for that angle using the unit circle or known values of cosine for standard angles.

Finally, calculate \( \sec(\theta) \) by taking the reciprocal of the cosine value found in the previous step. If \( \cos(\theta) = 0 \), then \( \sec(\theta) \) is undefined.

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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 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.

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