I think it may be time. We’ve looked at angles, we’ve spun an object. It’s time for: soh cah toa. Yes, soh cah toa. This seemingly nonsensical word is actually the foundation for a lot of computer graphics work. A basic understanding of trigonometry is essential if you want to calculate an angle, figure out the distance between points, work with circles, arcs, or lines. And soh cah toa is a mnemonic device (albeit a somewhat absurd one) for what the trigonometric functions sine, cosine, and tangent mean.
- soh: sine = opposite / hypotenuse
- cah: cosine = adjacent / hypotenuse
- toa: tangent = opposite / adjacent
Take a look at the above diagram again. There’s no need to memorize it, but make sure you feel comfortable with it. Draw it again yourself. Now let’s draw it a slightly different way:
See how we create a right triangle out of a vector? The vector arrow itself is the hypotenuse and the components of the vector (
y) are the sides of the triangle. The angle is an additional means for specifying the vector’s direction (or “heading”).
Because the trigonometric functions allow us to establish a relationship between the components of a vector and its direction + magnitude, they will prove very useful throughout this course. We’ll begin by looking at an example that requires the tangent function.