Trigonometry contains a set of functions that behave in very interesting ways. Unlike linear functions that form a straight line, trig functions like sine and cosine create a repeating up and down motion. This is perfect for animating anything that exhibits repetitive motion. Some examples would be a merry-go-round, a ferris wheel, a walking or running character, and the solar system.
Advanced algebra provides a tool called a matrix that allows animators to easily rotate, skew, flip, scale, and translate objects in 3D space. A matrix is a rectangular array defined by columns and rows. It contains a lot of information in a very streamlined format. The elements of the matrix determine what it can accomplish. Matrices make it possible to project a three dimensional space onto a two dimensional screen.
Calculus and Beyond
Have you ever watched a computer animated movie and thought that everything seemed so realistic? You just want to reach out and pet the puppy or jump into the glistening blue water. The realism in computer animation comes from a branch of math called Calculus. Everything from the motion of an insect's antennae to an ogre's jiggling belly can be fully controlled by very complex families of functions.