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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:
2
2
)
cos(
y
x
r
r
x
+
=
⋅
=
θ
=
⋅
=
−
x
y
r
y
1
tan
)
sin(
θ
θ
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
y
x
z
x
y
y
z
y
x
x
2
2
1
1
2
2
2
tan
)
cos(
tan
)
sin(
)
sin(
)
cos(
)
sin(
φ
φ
ρ
θ
θ
φ
ρ
ρ
θ
φ
ρ
To change the coordinate system in your calculator, follow these steps:
