Question about cylindrical Coordinates

[PsychonautQQ]

I'm confused why when using cylindrical coordinates three unit vectors are needed. My book says that the three unit vectors are one for the radial direction which is bound to the xy plane and then a unit vector in the z direction. It goes on to say that there is another unit vector associated with an angle from the x-axis to the point, but isn't this unit vector just redundant information from the radial unit vector? Why is it necessary?

 

[Matterwave]

In three dimensions, you will always need (at least) 3 coordinates (each of which would correspond to a unit vector), this is irrespective of what coordinate system you're using.

The three unit vectors in cylindrical coordinates are $(\hat{r},\hat{\theta},\hat{z})$. r and theta act exactly as they do in polar coordinates, and z moves you up and down the z-axis.

Maybe if this confuses you, just think about polar coordinates. Certainly you don't think that polar coordinates only need r and not theta?