HP 48gII User Manual Page 289

Graphing calculator.

„Ô5 ‚í ~‚6 25 ‚í 2.3
Before pressing `, the screen will look as in the left-hand side of the
following figure. After pressing `, the screen will look as in the right-hand
side of the figure (For this example, the numerical format was changed to Fix,
with three decimals).
Notice that the vector is displayed in Cartesian coordinates , with components
x = r cos(θ), y = r sin(θ), z = z, even though we entered it in polar coordinates.
This is because the vector display will default to the current coordinate system.
For this case, we have x = 4.532, y = 2.112, and z = 2.300.
Suppose that we now enter a vector in spherical coordinates (i.e., in the form
(ρ,θ,φ), where ρ is the length of the vector, θ is the angle that the xy projection
of the vector forms with the positive side of the x-axis, and φ is the angle that ρ
forms with the positive side of the z axis), with ρ = 5, θ = 25
o
, and φ = 45
o
.
We will use:„Ô5 ‚í ~‚6 25 í
~‚6 45
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.
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