# Introduction The unit circle has a center a $(0, 0)$, and a radius of $1$ with no defined unit. Sine and cosine can be used to find the coordinates of specific points on the unit circle. **Sine likes $y$, and cosine likes $x$.** When sine is positive, the $y$ value is positive. When $x$ is positive, the cosine is positive. $$ cos(\theta) = x $$ $$ sin(\theta) = y $$ ## Sine and Cosine | Angle | $0$ ## The Pythagorean Identity The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions. $$ sin^2 \theta + cos^2 \theta = 1 $$ # Definitions | Term | Description | | ---------------- | ----------------------------------------------------------------------------- | | $\theta$ (theta) | Theta refers to the angle measure in a unit circle. | | $s$ | $s$ is used to the length of the arc created by angle $\theta$ on the circle. |