Find each exact function value. See Example 2.
tan 5π/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 allows us to define the sine, cosine, and tangent functions for all angles. Each point on the unit circle corresponds to an angle and provides the coordinates (cosine, sine) for that angle, which are essential for calculating trigonometric values.

Tangent Function

The tangent function, denoted as tan(θ), is defined as the ratio of the sine and cosine of an angle: tan(θ) = sin(θ) / cos(θ). It represents the slope of the line formed by the angle in the unit circle. Understanding how to compute the tangent of specific angles, especially those in different quadrants, is crucial for solving trigonometric problems.

Reference Angles

A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. It is used to simplify the calculation of trigonometric functions for angles greater than 90 degrees or less than 0 degrees. For example, the reference angle for 5π/6 is π/6, which helps in determining the exact values of sine, cosine, and tangent for angles in the second quadrant.