Properties of $y = \sin x$ and Its Graph
Big Idea: The sine function is one of the most fundamental functions in all of mathematics. It models periodic (repeating) phenomena — from sound waves and light to tides and seasons. Understanding its graph and properties is the key to unlocking trigonometry.
1. Definition Recap
For any angle $x$ (measured in radians), $\sin x$ is defined as the y-coordinate of the point on the unit circle corresponding to that angle. As the angle $x$ increases from $0$ to $2\pi$, the point traces the full circle, and the y-coordinate rises, falls, and returns — creating the classic sine wave.