Arc Length in Polar

Trigonometry · Axiom Academy

LESSON Arc Length in Polar Coordinates Measuring the distance along curves defined in polar form using integration In Cartesian coordinates, we might use the familiar arc length formula. But in polar coordinates, points are defined by (r, θ) rather than (x, y). As we move along a polar curve, both the radius and angle are changing. For a polar curve r = f(θ) traced from θ = α to θ = β, the arc length is: This formula combines two effects: r² accounts for the circular arc at each radius, while (dr/dθ)² accounts for the change in radius as we move along the curve. 3. Interactive Measurement Tool Explore how arc length changes for different polar curves. Adjust the curve type and angle range to see how the formula works in practice.

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