# Anne Fibian Rides the Paddle Wheel

- Author:
- Terri Rehner

- Topic:
- Circle, Cosine, Sine, Trigonometry, Unit Circle

Anne Fibian is a frog who grabs onto a paddle wheel of a riverboat. The horizontal axle of the wheel is at water level. She begins her journey at the top of the paddle wheel clinging tightly to the paddle. The wheel is slowly spinning at one revolution every 6 minutes. This means that Anne is underwater 3 minutes during each rotation/revolution. Time is measured in seconds which means that the wheel is turning through 1 degree per second. The height above the surface of the water is measured in meters and may be either positive (above the water) or negative (below the water). The distance from the vertical axis (measured in meters) of the wheel may also be either positive (right of the vertical axis) or negative (left of the vertical axis).

1. Find the radius of the paddle wheel.
2. Describe the situation when the height is 0.
3. Use the slider to watch Anne Fibian travel around the paddle wheel. Describe in words the height of Anne with respect to
the water.
4. Explain which graph on the right represents the height above the water.
5. Find the function with respect to time that models height above the water. What is the significance of each parameter
in your function? Can you find another function?
6. Describe the situation when the distance from the vertical axis is 0.
7. Describe in words the distance from the vertical axis for Anne as she goes around the paddle wheel.
8. Explain which graph on the right represents the distance from the vertical axis.
9. Find the function with respect to time that models the distance from the vertical axis. What is the significance of each
parameter in your function? Can you find another function?
10. When you moved the slider and Anne Fibian moved along the paddle wheel, some points were created modeling her path.
Find an equation that relates the height vs distance from the vertical axis. How is this equation relate to the other
equations you found.
11. When Anne rotated, describe orientation and isometry of her image.