Learning Polar Graphing

Simulating Polar Graphs in GeoGebra -- Learning the basics of GeoGebra polar forms (Polar Points)

"In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction." Wikipedia

Many users using GeoGebra tend to graph in rectangular or Cartesian coordinate form where:

  • points are defined by giving the x-coordinate and y-coordinate of the point (x, y): A = (6, -8)
  • lines in the slope-intercept form: y = m x + b
  • lines in standard form: a x + b y = c
  • any standard functions of x: f(x) = <function of choice>
  • standard functions include linear, quadratic, cubic, ..., trigonometric, exponential, ..., conics, ...

There are some basic polar graphing facilities built into GeoGebra. These include:

  • points in polar form for example 4 units from the center at an angle of 45° is written: B = (4; 45°). {The semicolon indicates that the point is in polar form.}
  • lines in polar form go from a point in the direction of a vector, Line[Point M, Direction vector v] {see Page 2}
  • circles can be easily drawn in polar form from a point with a radius, Circle[Point M, Number r], a circle with radius 5: Circle[(1,4), 5]

To draw a circle with a center at Point(4,5) and radius = 3, enter the following command in the input line: Circle[(4, 5), 3]

Periodically you will want Press the Recycle Icon on the upper right to clear the worksheet.

{Try the above entries and others below prior to proceeding to Page 2.}

  Below are several exercises to allow you to master the above commands.
  • P = (3; cos(45°))
  • O = (4; 45°)
  • L = (4; 1)
  • A =
  • R =
  • l = Line[ A, (cos(45°), sin(60°)) ]. using Point A above or placed with mouse
  • i =
  • n =
  • e =
  • s =
  • c = Circle[L, 5]
  • u = Circle[(1,4), 5]
  • r =
  • v =

This instructional construction is for students and teachers to learn how to use parametric curve command to graph polar graphs.

The original version of this set of files is located here. This page is an improvement that provides more assistance for students.

A. B. Cron, Created with GeoGebra