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The figure below shows the transformation of the vector from spherical to
Cartesian coordinates, with x = ρ sin(φ) cos(θ), y = ρ sin (φ) cos (θ), z = ρ
cos(φ). For this case, x = 3.204, y = 1.494, and z = 3.536.
If the CYLINdrical system is selected, the top line of the display will show an R∠
Z field, and a vector entered in cylindrical coordinates will be shown in its
cylindrical (or polar) coordinate form (r,θ,z). To see this in action, change the
coordinate system to CYLINdrical and watch how the vector displayed in the
last screen changes to its cylindrical (polar) coordinate form. The second
component is shown with the angle character in front to emphasize its angular
nature.
The conversion from Cartesian to cylindrical coordinates is such that r =
(x
2
+y
2
)
1/2
, θ = tan
-1
(y/x), and z = z. For the case shown above the
transformation was such that (x,y,z) = (3.204, 2.112, 2.300), produced (r,θ,z)
= (3.536,25
o
,3.536).
At this point, change the angular measure to Radians. If we now enter a vector
of integers in Cartesian form, even if the CYLINdrical coordinate system is
active, it will be shown in Cartesian coordinates, e.g.,
This is because the integer numbers are intended for use with the CAS and,
therefore, the components of this vector are kept in Cartesian form. To force the
conversion to polar coordinates enter the vector components as real numbers
(i.e., add a decimal point), e.g., [2., 3., 5.].
With the cylindrical coordinate system selected, if we enter a vector in spherical
coordinates it will be automatically transformed to its cylindrical (polar)