The Trig You Need for Calculus: Definition of Trig Functions

There are two elementary ways of defining the trigonometric functions, and a student of calculus must be familiar with both.

The first way is to define the trig functions as ratios of the lengths of the sides of a right triangle.

righttri

trig_defs

The second way is to define cosine and sine of an angle as the x and y coordinates, respectively, of the point at which its ending side intersects the unit circle. Using identities from above, the remaining trig functions can be evaluated using the values of sine and cosine. This is the most useful way of evaluating trig functions for angles whose ending side lies on the x-axis or y-axis.

unitcircle