The question I'm having trouble with is..
Plot the point $(1, \frac{\pi}{4})$. Then find two other pairs of polar coordinates of this point, one with $r > 0$ and one with $r < 0$.
I am not sure how to find an alternative polar coordinate for $(1, \frac{\pi}{4})$ with a different $r$ that is on the same point in the graph.
I could understand if I was supposed to find a different angle $\theta$, since $\frac{\pi}{4}=2\pi+\frac{\pi}{4}=4\pi+\frac{\pi}{4}=...$ but I am not sure how to find an alternative $r$ for the same point, that isn't equal to $1$.
I thought $r$ was just the distance from the origin $O$?
The fact that they want one answer with $r<0$ indicates that you should consider adding an odd multiple of $\pi$ to your $\theta$ value. Try $r=-1$ and $\theta = 5\pi/4$.