Trigonometry for Animation - HTML5 Animation with JavaScript - page 34

What is trigonometry?

Trigonometry is the study of triangles and the relationship of their sides and angles. If you look at any
triangle, you see that it has three sides and three angles (hence, the name tri-angle). It happens that these
sides and angles have specific relationships. For example, if you take any triangle and make one of the
angles larger, the side opposite of that angle gets longer (assuming the other two sides stay the same
length). Also, the other two angles get smaller. Exactly how much each of these things changes takes a bit
of calculation, but the ratios have all been figured out and codified.

A specific type of triangle has one of its angles equal to exactly 90 degrees. This is called a right-angle
triangle and is indicated by a little square in the corner of that angle. It happens that in a right-angle
triangle, the various relationships are far simpler and quite easy to figure out with some basic formulas.
This makes a right-angle triangle a useful construct, and all of the trigonometry in this chapter, and most of
what you see in the rest of the topic, deals with right-angle triangles.

Angles

Because trigonometry is mostly about angles, let's look at that subject first. An angle is simply the shape
formed by two intersecting lines, or the space in between those lines. The more space, the higher the
measurement of the angle. Actually, two intersecting lines form four angles, as you can see in Figure 3-1.

Angle A

Angle D

Angle C Angle B

Figure 3-1. Two lines form four angles.

Radians and degrees

The two major systems for measuring angles are degrees and radians. You are probably familiar with
degrees, and could probably draw a 45- or 90-degree angle if I asked you to. The system of 360 degrees
in a circle has become a part of our culture. People say they're “doing a 180,” meaning “going in the
opposite direction,” even when we are not talking about physical direction, but referring to taking an
opposite viewpoint. But it turns out that computers have a lot more affinity for radians when it comes to
representing angles. So, like it or not, you need to know about radians.

A radian is equal to approximately 57.2958 degrees. At first glance, that number may seem arbitrary, but
there is some actual logic to it. A full circle, or 360 degrees, works out to 6.2832 radians. Remember pi—