34 lines
1.6 KiB
Markdown
34 lines
1.6 KiB
Markdown
# 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 | $0$ | $\frac{\pi}{6}$ or $30 \degree$ | $\frac{\pi}{4}$ or $45\degree$ | $\frac{\pi}{2}$ or $90\degree$ |
|
|
| ------ | --- | ------------------------------- | ------------------------------ | ------------------------------ |
|
|
| Cosine | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ |
|
|
| Sine | 0 | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ | <br>$1$ |
|
|
|
|
|
|
|
|
Finding a reference angle:
|
|
|
|
| Quadrant | Formula |
|
|
| -------- | --------------------- |
|
|
| 1 | $\theta$ |
|
|
| 2 | $180\degree - \theta$ |
|
|
| 3 | $\theta - 180\degree$ |
|
|
| 4 | $360\degree - \theta$ |
|
|
# 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. | |