Give the exact value of each expression. See Example 5. sec 45°

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 evaluating secant values, especially for common angles like 45°, where the cosine value is known.

Special Angles in Trigonometry

In trigonometry, special angles such as 0°, 30°, 45°, 60°, and 90° have specific sine, cosine, and tangent values that are commonly used. For example, at 45°, both sine and cosine equal √2/2, which simplifies calculations for secant and other trigonometric functions.

Unit Circle

The unit circle is a fundamental concept in trigonometry that provides a geometric interpretation of trigonometric functions. It is a circle with a radius of one centered at the origin of a coordinate plane, where the coordinates of any point on the circle correspond to the cosine and sine of the angle formed with the positive x-axis. This visualization aids in understanding the values of trigonometric functions at various angles.