HP 48gII User's Manual
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The coordinate system selection affects the way vectors and complex numbers
are displayed and entered. To learn more about complex numbers and
vectors, see Chapters 4 and 9, respectively.
Two- and three-dimensional vector components and complex numbers can be
represented in any of 3 coordinate systems: The Cartesian (2 dimensional) or
Rectangular (3 dimensional), Cylindrical (3 dimensional) or Polar (2
dimensional), and Spherical (only 3 dimensional). In a Cartesian or
Rectangular coordinate system a point P will have three linear coordinates
(x,y,z) measured from the origin along each of three mutually perpendicular
axes (in 2 d mode, z is assumed to be 0). In a Cylindrical or Polar
coordinate system the coordinates of a point are given by (r,θ,z), where r is a
radial distance measured from the origin on the xy plane, θ is the angle that
the radial distance r forms with the positive x axis -- measured as positive in a
counterclockwise direction --, and z is the same as the z coordinate in a
Cartesian system (in 2 d mode, z is assumed to be 0). The Rectangular and
Polar systems are related by the following quantities:
22
)cos( yxrrx +=⋅= θ
=⋅=
−
x
y
ry
1
tan)sin( θθ
z
z
=
In a Spherical coordinate system the coordinates of a point are given by
(ρ,θ,φ) where ρ is a radial distance measured from the origin of a Cartesian
system, θ is an angle representing the angle formed by the projection of the
linear distance ρ onto the xy axis (same as θ in Polar coordinates), and φ is
the angle from the positive z axis to the radial distance ρ. The Rectangular
and Spherical coordinate systems are related by the following quantities:
+
=⋅=
=⋅⋅=
++=⋅⋅=
−
−
z
yx
z
x
y
y
zyxx
22
1
1
222
tan)cos(
tan)sin()sin(
)cos()sin(
φφρ
θθφρ
ρθφρ
To change the coordinate system in your calculator, follow these steps: