How do you find the slope of the tangent line to a polar curve?

Heidy Haley

Heidy Haley

Answered question

2023-02-12

How to find the slope of the tangent line to a polar curve?

Answer & Explanation

oipineonz5j

oipineonz5j

Beginner2023-02-13Added 9 answers

A polar equation of the form r = r ( θ ) can be converted into a pair of parametric equations
{ x ( θ ) = r ( θ ) cos θ y ( θ ) = r ( θ ) sin θ .
The slope m of the tangent line at θ = θ 0 can be expressed as
m = d y d x θ = θ 0 = d y d θ θ = θ 0 d x d θ θ = θ 0 = y ( θ 0 ) x ( θ 0 ) .

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