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

1 Answer
Alan P.
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.

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From the graph:
# r = sqrt(4^2 + (-1)^2) = sqrt(17)#
and
#theta = arctan((-1)/4)#

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 #[0,2pi)# range.

Depending upon the version used you will typically get
#arctan((-1)/4) = -0.245# (radians)
or
#arctan((-1)/4) = -14.040# (degrees)

Add #2pi# or #360^o# respectively to get the "correct" answer.

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