Math and physics › Angles and rotations
Angles, sine and cosine: a point on a circle
Know first: Vectors: arrows you can add
An angle is a turn, and sine and cosine are the two coordinates of a point running around a circle. Almost all the trigonometry a game needs follows from this one picture. It places torches in a ring around a campfire, swivels a turret toward its target, sends a gust of wind through grass and makes a light flicker. Along the way: degrees and radians, the point on the circle, the way back from an arrow to an angle, and waves.
Why this matters
Trigonometry usually starts with a triangle: “the sine is the opposite side divided by the hypotenuse.” That rule does not show where rotation and waves come in, so you end up memorizing the formulas.
Games use sine and cosine for exactly two things: rotation and repetition. That covers a turret or a compass needle, objects in a ring, orbits, grass in the wind, a boat on the waves and a flickering fire.
Read the lesson on vectors first. The cosine already appeared in the lesson on the dot product as “the part along”; here you will see where it comes from.