Exploration: Interactive Unit Circle
- Author:
- cesarmathjuarez, J Rothman
- Topic:
- Circle, Cosine, Sine, Triangles, Trigonometry, Unit Circle
Directions:
An interactive for exploring the coordinates and angles of the unit circle, as well as finding the patterns among both. Explore the unit circle by moving the block dot around the unit circle. After exploring, answer the questions below the unit circle to earn credit for your classwork.
1. Observations and Patterns
As you rotated around the unit circle from 0 degrees to 360 degrees, what did you notice? What changed? What stay the same? What patterns do you observe? Be as specific as you possibly can.
2. The Radius
What is the radius of the unit circle? How does this radius connect to the maximum and minimum values of the sine and cosine functions? Click on the link in Question 3. if you are unsure.
3. Graphs of Sine and Cosine
4. Relationship of Sine
What relationship does the Sine function have with the unit circle? Notice how the graph of sine is changing when the angle of the unit circle changes!
5. Relationship of Cosine
What relationship does the Cosine function have with the unit circle? Notice how the graph of sine is changing when the angle of the unit circle changes!