Question

for what values of theta on the polar curve r = theta, with 0 <= theta <= 2pi, are the tangent lines horizontal? vertical?

Answer 1

The tangent lines are vertical when \(\dfrac{dx}{dy}\) is 0 and horizontal when \(\dfrac{dy}{dx}\) is 0.

Finding expressions for these in terms of \(r\) and \(\theta\) is a matter of some derivation, which I've done here: http://openstudy.com/users/sithsandgiggles#/updates/5480b993e4b0a93bce3d573e