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

1 Answer
Wataru
Oct 9, 2014

A polar equation of the form r=r(theta) can be converted into a pair of parametric equations

{(x(theta)=r(theta)cos theta),(y(theta)=r(theta)sin theta):}.

The slope m of the tangent line at theta=theta_0 can be expressed as

m={dy}/{dx}|_{theta=theta_0}={{dy}/{d theta}|_{theta=theta_0}}/{{dx}/{d theta}|_{theta=theta_0}}={y'(theta_0)}/{x'(theta_0)}.

I hope that this was helpful.

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