Definition of Trigonometric Functions With trigonometric ratios of acute angles in triangles, we are limited to angles between 0 and 90 degrees. We now define the trigonometric functions in terms of angles in standard form in the coordinate plane.

Definition: Let an angle x (in radian measure) be in standard position. Let a point P with coordinates (a,b) be the point of intersection of the terminal side of the angle and the circle of radius r (were r > 0). Then:

Note that if the radius of the circle is 1 we have the following:

We call the circle of radius 1 the unit circle, and on the unit circle we have …

 Example 1: Find the values of the six trigonometric functions for angle x with the terminal side containing the point ( −3,−5). The distance from the given point to the origin (0,0), which is radius r, is given by …

 Example 2: Let x have a terminal side containing point (a,b), where the point is in quadrant II, and sin x = 2/7.

Since the point is in quadrant II, the value of a must be negative, and we have …