Right Triangles

There are several ways to actually define the six trigonometric functions. We choose to do so using right triangles. (Recall that a right triangle is a triangle with an angle measuring 90°.)

Let's begin with an angle which is between 0° and 90° . (This will simplify our discussion for now; we can extend our definition to any angle later.) Assume the angle is in standard position, so that it is positioned in the xy-plane as follows:

We now define three terms which correspond to the three ``legs'' of the triangle. We say that the hypotenuse is the leg opposite the right angle, while the opposite side is the side opposite and the adjacent side is the side adjacent to the angle in question.

Recall that we know a very special relationship between the lengths of these three legs. It is known as the Pythagorean Theorem:

There are six possible ratios of these three sides, and these six ratios are used to define the six trigonometric functions.