Question

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

Answer 1

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.