In this lesson, we break down how to confidently convert between polar and rectangular forms. You’ll learn how to take a single polar coordinate and express it in two different ways—one with a positive radius and one with a negative radius—so you fully understand how points can be represented multiple ways in polar coordinates.
We also walk step-by-step through converting polar coordinates into rectangular form using the relationships below:
x=rcosθ,y=rsinθ
Then, we shift to converting rectangular equations into polar form by using substitution and identities. You’ll see a full example with a circle:
x² + (y − 3)² = 9
and learn how to rewrite it entirely in terms of r and θ.
By the end of this lesson, you’ll be able to:
Convert polar coordinates to rectangular coordinates
Represent a polar point in multiple ways (positive and negative r)
Convert rectangular equations into polar form
Recognize how familiar shapes (like circles) look in polar coordinates
Perfect for Precalculus students looking to strengthen their understanding of polar relationships and build confidence with conversions!
