# How do you change (4, -1) from rectangular to cylindrical coordinates between [0, 2π)?

Mar 4, 2015

I will assume you meant "polar coordinates" since cylindrical coordinates are 3-dimensional and you have only supplied 2-dimensional Cartesian coordinates.

From the graph:
$r = \sqrt{{4}^{2} + {\left(- 1\right)}^{2}} = \sqrt{17}$
and
$\theta = \arctan \left(\frac{- 1}{4}\right)$

Note that standard arctan functions will return a value which will need to be adjusted to compensate for the point being in the IV quadrant so $\theta$ will fall in the $\left[0 , 2 \pi\right)$ range.

Depending upon the version used you will typically get
$\arctan \left(\frac{- 1}{4}\right) = - 0.245$ (radians)
or
$\arctan \left(\frac{- 1}{4}\right) = - 14.040$ (degrees)

Add $2 \pi$ or ${360}^{o}$ respectively to get the "correct" answer.