While plotting polar coordinate system graphs, should we include the negative of angle $\theta$?

For example, while plotting $r=\theta$ for negative values the spiral comes out to be reverse of the graph plotted using positive values. Upon searching in google I find only one spiral. So are both spirals part of the curve?

  • 3
    $\begingroup$ There's no reason to omit negative values of $\theta$, other than that the pictures are sometimes less pretty. $\endgroup$ – Aaron Montgomery Oct 30 '17 at 17:46
  • 2
    $\begingroup$ Negative values of $\theta$ are perfectly fine. Often times when doing integrals in polar coordinates, it is convenient to use a parameterization with negative values rather than positive ones. $\endgroup$ – superckl Oct 30 '17 at 17:49

It's not really about $\theta$, which of course can be both positive or negative. Rather it's about the values of $r$ — should we allow negative values of $r$ or not? And this is not really a mathematical question, but rather a matter of convention. Most textbooks I've seen allow both positive and negative values of $r$. However, some require that $r$ must be non-negative ($r\ge0$).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.