Unit circle
01 / 04 · Start with the radius and the coordinates
Predict firstAfter rotating 30° from the positive x axis, does each coordinate of the point increase or decrease?
Radius r = 1
Guided lesson
Understand the trigonometric functions as the coordinates of one rotating point.
Prerequisites: Familiarity with plane coordinates; an angle measures how far something has turned.01 / 04
Start with the radius and the coordinates
Predict firstAfter rotating 30° from the positive x axis, does each coordinate of the point increase or decrease?
The radius of the unit circle is 1. The angle θ is measured counterclockwise from the positive x axis, and the point on the circle is P = (cos θ, sin θ). The blue projection gives the x coordinate and the red projection the y coordinate.
How to observe
- Drag the point around the circle and watch the right triangle
- Turn through four quadrants and track the signs of sine and cosine
- Pause at special angles and compare the projected lengths
Model notes
The radius is 1. The projections are signed coordinates; sine and cosine are not side lengths that stay positive.
SourcesOpenStax · Unit circle