In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of


0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6


Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
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In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
sec 11𝜋/6

Key Concepts

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is fundamental in trigonometry as it provides a geometric representation of the sine, cosine, and tangent functions. The coordinates of points on the unit circle correspond to the cosine and sine values of angles measured in radians, allowing for easy calculation of trigonometric functions.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and secant, relate the angles of a triangle to the lengths of its sides. For example, the secant function is defined as the reciprocal of the cosine function. Understanding how to evaluate these functions at specific angles, particularly those corresponding to points on the unit circle, is crucial for solving trigonometric problems.

Radians and Angle Measurement

Radians are a unit of angular measure used in trigonometry, where one radian is the angle subtended at the center of a circle by an arc equal in length to the radius. The unit circle divides angles into radians, making it essential to convert between degrees and radians when solving trigonometric problems. Familiarity with common radian values, such as π/6, π/4, and π/3, is important for evaluating trigonometric functions accurately.