Find each exact function value. ​See Example 3.​
tan 5π/3

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 for the definition of sine, cosine, and tangent functions based on the coordinates of points on the circle. For any angle θ, the coordinates (cos(θ), sin(θ)) represent the cosine and sine values, respectively, which are essential for calculating trigonometric functions like tangent.

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 tangent values using the unit circle is crucial for finding exact function values for specific angles, such as 5π/3.

Reference Angles

Reference angles are the acute angles formed by the terminal side of an angle and the x-axis. They help simplify the calculation of trigonometric functions for angles greater than 90 degrees. For example, to find tan(5π/3), one can determine its reference angle, which is 2π/3, and use the properties of the tangent function in the appropriate quadrant to find the exact value.