Trigonometry for Games and Graphics · Reference
Glossary
The canonical vocabulary for this course — one tight definition per term.
The shared language for this course. Every lesson uses these words and no synonyms, so the vocabulary compresses rather than sprawls.
Terms are added here once you can use them correctly — not when they are first introduced. A short glossary is a truthful one.
Angles
Radian: The angle whose arc along the rim equals the radius. A full turn is 2π radians. Avoid: Rad measure, natural angle
Degree: One 360th of a full turn. A display and API unit only — never the unit you calculate in. Avoid: Deg, angle (unqualified)
Turn: One complete revolution: 360°, or 2π radians. The unit to think in when spacing things evenly around a circle. Avoid: Revolution, cycle, loop
The circle
Unit circle: The circle of radius 1 centred at the origin. The reference frame in which every angle has a single unambiguous point. Avoid: Trig circle, reference circle
Cosine (cos θ): The x-coordinate of the point at angle θ on the unit circle. Always between −1 and 1. Avoid: Adjacent over hypotenuse
Sine (sin θ): The y-coordinate of the point at angle θ on the unit circle. Always between −1 and 1. Avoid: Opposite over hypotenuse
Quadrant: One of the four quarters of the plane, numbered I to IV counterclockwise from the upper right. Determines the sign pair of cosine and sine. Avoid: Corner, region
Motion
Unit vector:
A vector of length 1, carrying direction and no magnitude. (cos θ, sin θ) is the unit
vector pointing at angle θ.
Avoid: Normalised vector, heading vector, direction (unqualified)
Screen space:
A coordinate frame in which +y points downward, as in raylib and LÖVE. Angles still obey
(cos θ, sin θ), but a growing θ appears to sweep clockwise.
Avoid: Y-flipped space, image coordinates
Ambiguities resolved
- “Angle” always means radians in this workspace. When degrees are meant, they are said explicitly and written with a degree sign.
- Angles are measured counterclockwise from the positive x-axis, unless a lesson states
otherwise. This is what
cos,sin, andatan2assume in every language here. - “Direction” always means a unit vector, never an angle. When an angle is meant, the word is “angle” or “heading”.