Exploring the Equation of a Circle Using the Pythagorean Theorem

This lesson explores how the Pythagorean theorem can be used to graph circles by understanding the definition of a circle. It introduces the unit circle, a circle with a radius of one unit centered at the origin, and explains how right triangles can be formed within it. The lesson covers how to calculate sine and cosine values using the unit circle and addresses common mistakes students make. Finally, it generalizes the circle equation using the Pythagorean theorem, showing how x squared plus y squared equals r squared represents a circle.

What is the definition of a circle?

Explain how the Pythagorean theorem relates to the unit circle.

What are the sine and cosine values for the reference angle theta in the context of the unit circle?

How can the Pythagorean theorem be used to represent all the points that make up a circle?

What is the more generic form of the formula for a circle when considering the radius?