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As with two dimensional space the standard
coordinate
system is called the Cartesian coordinate system. In the last two sections of this
chapter we’ll be looking at some alternate coordinates systems for three dimensional
space.
We’ll start off with the cylindrical coordinate system. This one is fairly simple as it is
nothing more than an extension of
polar coordinates
into three dimensions. Not only
is it an extension of polar coordinates, but we extend it into the third dimension just as
we extend Cartesian coordinates into the third dimension. All that we do is add a
z
on
as the third coordinate. The
r
and θ are the same as with polar coordinates.
Here is a sketch of a point in
.
The conversions for
x
and
y
are the same conversions that we used back in when we
were looking at polar coordinates. So, if we have a point in cylindrical coordinates
the Cartesian coordinates can be found by using the following conversions.
The third equation is just an acknowledgement that the
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 Fall '08
 prellis
 Cartesian Coordinate System

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