Parametric Curves

Instead of one equation, x and y are BOTH controlled by a third variable (θ)

How to Sketch

1. Pick θ values and make a table
2. Compute points (x(θ), y(θ))
3. Plot and connect in order (you are drawing a path not just a shape)

Convert parametric → Cartesian

The goal is to remove the parameter θ

1. Solve one equation for θ
2. Substitute it into y (or whatever you found) $y=g(θ)->y=g(x)$
3. Simplify

Convert polar → Cartesian

Polar → Cartesian

• $x=rcosθ$
• $y=rsinθ$