Cosine of theta describes how much of a direction lies along the horizontal when you move at an angle. If you imagine a right triangle with angle theta, cosine compares the side next to the angle with the longest side, giving a value between −1 and 1 as theta changes. This makes cosine perfect for modeling smooth, repeating motion: waves, oscillations, circular motion, and projections all naturally follow a cosine pattern. As theta increases, cosine doesn’t grow forever—it cycles, reflecting how