Find a cartesian equation for the curve and identify it. r = 3 cos(θ)

Solution:

Given that r = 3 cos(θ)

Multiplying throughout by r,

r² = 3r cos θ

Let x = r cos θ and y = r sin θ

This satisfies the equation x² + y² = r².

We get, x² + y² = 3r cos θ

x² + y² = 3x

⇒ x² + y² - 3x = 0 is the required cartesian form.

Find a cartesian equation for the curve and identify it. r = 3 cos(θ)

Summary:

The cartesian equation for the curve r = 3 cos(θ) is x² + y² - 3x = 0.