The sine function is one of the most important ideas in trigonometry. It comes from studying right triangles, where sine is the ratio of the side opposite an angle to the hypotenuse. More broadly, sine describes patterns of oscillation, rotation, and wave motion. Its graph is a smooth, repeating curve that goes up and down between –1 and 1, repeating every 360 degrees. Because of this, sine shows up in physics to model things like sound waves, vibrations, and circular motion. The cosine function