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

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?

• There's no reason to omit negative values of $\theta$, other than that the pictures are sometimes less pretty. – Aaron Montgomery Oct 30 '17 at 17:46
• 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. – 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 ($r\ge0$).