6-2 Trigonometry

What is trigonometry? Trigonometry is simply the study of the relationships between sides of a triangle. These triangles are drawn on a circle so that we can draw conclusions. Lets first study the circle, and then the triangles.

The Unit Circle (0,1) -,+ +,+ (-1,0) (1,0) -,- +,- (0,-1)

Terminal ray + θ -

These are the reference triangles

Trigonometric Functions y θ x

Trigonometric Functions y θ x

How do I put this all together? 1. Determine what quadrant the terminal ray lies in and draw it. Draw a line to the closest x axis (if you don’t, you will get the wrong answer) Label the sides, including signs, then determine function.

Examples Find Find sin π, cos π and tan π.

What did we learn with the last problem? If you land on an axis, there is no triangle. So instead of using sides of the triangle, use x, y and r. Unless otherwise specified, r = 1.