# 4.2 Defining the Trigonometric Functions

**Definitions of the Trigonometric Functions • Evaluating the Trigonometric Functions • The Unit Circle**

In this section, we define the six *trigonometric functions*. These functions are used in a wide variety of technological fields to solve problems involving triangles as well as quantities that oscillate repeatedly. The six trigonometric functions are defined below.

# DEFINITION OF THE TRIGONOMETRIC FUNCTIONS

Let (*x, y*) be any point (other than the origin) on the terminal side of the angle $\theta $ in standard position, and let `r` be the distance between the origin and the given point (see Fig. 4.10).

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