Polar Curves Example

AP Calculus · Axiom Academy

The rose curve has the following properties: The parameter n = 3 (odd), so there are 3 petals Each petal has maximum length r = 2 The first petal occurs from θ = -π/6 to θ = π/6 The curve passes through the origin at θ = 0, π/3, 2π/3, etc. Step 3: Find the Arc Length of One Petal Using the arc length formula for polar curves from θ = -π/6 to θ = π/6: ✓ Result: One petal of the rose curve has arc length ≈ 4.53 units This was computed by numerical integration of the arc length formula Step 4: Find the Slope of the Tangent Line At θ = π/6 (the tip of the first petal), find dy/dx: ✓ Key Insight: The tangent line at the tip of the petal is vertical, which makes geometric sense!

This is the written version of the interactive lesson above. See the full AP Calculus course.