Sin(x) and Cos(x) from the Unit Circle (3D)
- Ken Schwartz
Shows how the Unit Circle generates the sine and cosine functions from an angle on the Unit Circle
If we plot any angle in Standard Position on the x-y plane, its terminal side will intersect the Unit Circle at a single point (x, y). (The Unit Circle is a circle of radius 1 centered at the origin). If we imagine a right triangle formed by the points (0, 0), (x, 0), and (x, y), we see that the length of this triangle's "opposite" side is simply y, and the length of the "adjacent" side is simply x. The Unit Circle therefore provides a graphical method of finding sin() and cos(). The 3D view shows the x and y values of the intersection point over time, as changes. Thus these are the graphs of cos() and sin().