The trig functions can be defined using the measures of the sides of a right triangle. But they also have very useful definitions using the coordinates of points on a graph. First, let let the vertex of an angle be at the origin — the point (0,0) — and let the initial side of that angle lie along the positive x-axis and the terminal side be a rotation in a counterclockwise motion. Then, when the point (x,y) lies on a circle that’s intersected by that terminal side, the trig functions are defined with the following ratios, where r is the radius of the circle.