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.


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

The graph is angle theta with a terminal side that rises through (x, y) with length r, horizontal length x, and vertical length y. A dashed segment of y meets the x-axis at a right angle from (x, y).


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