Sketching the Sine & Cosine Graphs in Trigonometry

Sine and cosine are two fundamental functions that arise naturally when studying circles, waves, and periodic motion. They originate from geometry: when a point moves around a circle at a constant speed, the horizontal and vertical positions of that point change smoothly and repeat over time. These repeating patterns are described precisely by cosine (horizontal movement) and sine (vertical movement). Because of this geometric origin, sine and cosine are deeply connected to angles, rotations, an