How do you find four other pairs of polar coordinates for the point #T(1.5, 180^o)#?
Consider moving the angle around the axis multiple times. Also consider the effect of moving radially backwards instead of forwards.
Think of how the polar coordinate system works - you have a radius
So there's immediately one way in which a point can have more than one description in polar coordinates - by going around the angle more than once. So adding
Don't forget that we also go back around the angle full turns in the other direction, obtaining also an infinite number of negative angles that are equivalent to the point
The final way in which we can find alternate descriptions of a polar point is to consider making the radial coordinate
As before, we can find an infinite number of extra angular turns in both positive and negative directions. These give us alternate coordinate descriptions
We can describe these families of alternates more compactly: