Applet: Rectangular and Polar Coordinates

Drag point A to explore its rectangular and polar coordinates. Use the checkboxes to show or hide each representation. Move the angle slider to rotate A around the origin.

Discovery Questions

1. Drag point A into each quadrant. How do the signs of its rectangular coordinates relate to its polar angle?
2. Choose three positions for A. Compare r cos θ with x. What relationship do you discover? Use it to rewrite r(1 + 2 cos θ) = 8 using only r and x.
3. For the same positions, compare r² with x² + y². What relationship do you discover? Use this and your answer to Question 2 to express r = 8/(1 + 2 cos θ) in rectangular coordinates.

← Return to Assignments