Given the polar curve, r + cos(2 theta), How would I go about finding all the points, (r,theta) (r>=0) (0<=theta<2pi) where the tangent line is a) horizontal and b) vertical? I think there are 6 sets for each one.

The slope is the derivative, so derive your curve and find where the derivative is 0.

Did you mean to say that your curve is r = cos (2 theta)?

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username: need2passCalcIII



This post was edited by thesnipa on Jan 26 2016 12:30pm

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You are correct, there are 6 sets for each.



Your problem is similar to this one. Google is your BFF. That or Wolfram Alpha.




You should note that if you move r to the other side of the equation, you get r = -cos(2theta), which is almost exactly the same problem. Instead of plugging in pi/2, solve the parametric derivatives for when they are zero to get your answers.

This post was edited by Dontrunaway on Jan 27 2016 08:13pm