CalcRef

Parametric, Polar & Vectors · Polar Coordinates

Polar Curve Slope

dydx=r′sin⁡θ+rcos⁡θr′cos⁡θ−rsin⁡θ\frac{dy}{dx} = \frac{r'\sin\theta + r\cos\theta}{r'\cos\theta - r\sin\theta}

The slope of a polar curve at a given angle θ. Derived from x = r cos θ, y = r sin θ using the parametric derivative formula.

Worked examples

Find the slope of r = 1 + cos θ at θ = π/2.
  1. r' = -sin θ. At θ = π/2: r = 1, r' = -1
  2. dy/dx = (-1·sin(π/2) + 1·cos(π/2))/(-1·cos(π/2) - 1·sin(π/2))
  3. = (-1 + 0)/(0 - 1) = -1/(-1) = 1

Answer: 1

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