In polar coordinates, r represents the distance of the point from the origin, and q (theta) represents the angle, measured in radians counterclockwise from the positive x-axis, between the positive x-axis and the ray from the origin to the point.
Everything
you need to know about converting between rectangular and polar coordinates
is in this picture:
Your calculator will convert rectangular coordinates to polar coordinates and vice versa on the HOME screen.
You need
to type a comma between the coordinates, even though it doesn't show up
in the history area.
The square
brackets are 2nd comma and 2nd divides. You need the square
brackets because the calculator thinks of points as vectors.
You can
find the Polar, together with the little triangle, in the CATALOG
under P, or buried deep in the MATH (2nd 5) menu, in the Vector
ops submenu of the Matrix menu. On the TI-92+, it's faster to type it;
the triangle is 2nd Y.
To convert
from polar coordinates to rectangular coordinates, just enter the polar
coordinates.
You need
a comma between the two coordinates (even though it doesn't show on the
screen) and an angle symbol before the angle.
The angle
symbol is marked on the keyboard in yellow.
If you want
your angles in degrees, the degree symbol is also marked on the keyboard.
You can also change Angle to DEGREE on the MODE
screen, but don't forget to change it back to RADIAN.
If you're in DEGREE mode and don't want to change to RADIAN mode but still
want to enter an angle in radians, enter a radian symbol ( r )
after the number.
The ris in the CATALOG, but
not under R. It's with the symbols before A. It's also in the Angle submenu
of the MATH (2nd 5) menu.
If you change
Vector Format from RECTANGULAR to CYLINDRICAL or SPHERICAL on the MODE
screen, points in the plane are automatically displayed in polar coordinates
(so converting from rectangular to polar coordinates is automatic.) If
you then want to convert to rectangular coordinates, you need Rect
from the CATALOG or MATH, Matrix, Vector ops
menu.
Graphing
in polar coordinates requires changing the Graph
mode to POLAR.
Even when
the Graph mode is POLAR, the cursor coordinates on the GRAPH
screen (for Zoom or Trace,
for example) are in rectangular coordinates.
To change
these to polar coordinates, you need to go the Graph
Format menu.
(You can
change Coordinates to POLAR even when the Graph mode is FUNCTION, which
is likely to cause confusion.)
In POLAR
mode, the Y= screen asks you to express r
as a function of theta. The
theta key is on the keyboard,
shown in the pictures above.
The calculator will also handle Cylindrical and Spherical coordinates in three dimensions.
The cylindrical
coordinates of a point are r, theta, and z. The spherical
coordinates of a point are rho, theta, and phi.
Everything
you need to know about the relationships among these coordinates and the
rectangular x,
y, and z coordinates is in this picture:
Theta
and phi are angles; theta means the same in cylindrical and spherical
coordinates as it does in polar coordinates.
Phi is the
angle, measured in radians down from the positive z-axis, between the positive
z-axis and the ray from the origin to the point.
Rho
is the distance between the point and the origin.
To convert
from rectangular to cylindrical or spherical coordinates, you need the
commands shown.
Again, they're
in the CATALOG under C and S or buried in the
MATH (2nd 5) menu.
You do need
to type the commas between the coordinates, even though they don't show.
Converting
from cylindrical or spherical coordinates back to rectangular is automatic;
just enter the cylindrical or polar coordinates.
The calculator
tells the difference by whether there's an angle symbol before the second
coordinate or before the last two coordinates.
You can
enter the angles in radians or in degrees. (The angle and degree symbols
are accessible from the keyboard; see the pictures above.)
You can set the Vector Format to CYLINDRICAL or SPHERICAL on the MODE menu. Then vectors appear automatically in the format you choose (or in polar coordinates in two dimensions.) To convert to rectangular coordinates, you need the Rect command, in the CATALOG.