The current GeoGebra has a polar graph display, but no basic polar equation format; however, one can create or simulate polar grids using GeoGebra's capability to graph parametric equations. Polar equations are relatively easy to write parametrically using x = r cos(theta) and y = r sin(theta). An expression for r will be substituted into the Parametric Curve Command allow us to graph polar equations. GeoGebra contains commands that will assist us in creating the polar grid. Points: A = (pole; angle) Circle[Point M, Number r] {Page 1} Line[Point, Direction vector v], and {Page 2} Sequence[Expression, Variable i, Number a, Number b, <Increment>] {Page 3} polarCircles = Sequence[Circle[(0, 0), k / 2], k, 1, 20] radialLines = Sequence[Line[(0, 0), (cos(a), sin(a))], a, 0, 175°, 15°] The Parametric Curve Command allows us to create or graph polar functions. Curve[Expression e1, Expression e2, Parameter t, Number a, Number b] Yields the Cartesian parametric curve for the given x-expression e1 and y-expression e2 (using parameter t) within the given interval [a, b]. r(x) = 1 {hide this line, this function will allow you to enter polar equations} Curve[r(i) cos(i), r(i) sin(i), i, 0, 2 pi] {this will draw a circle of radius one}
Cardioids r(x) = a (1 - cos(x)), vary a by using a slider Rose Curves r(x) = a cos(b x), vary a and b by using a sliders Rose Curves r(x) = a sin(b x), vary a and b by using a sliders Rose 'Style' Curves r(x) = c + a * sin(b * x), vary a, b, and c by using a sliders Lemniscates r(x) = sqrt(a2 cos(2 x)), vary a by using a slider Limacons r(x) = a cos(x), vary a by using a slider Equiangular Spiral r(x) = e^(a x), vary a by using a slider Spiral of Archimedes r(x) = a x, vary a by using a slider Lituus r(x) = sqrt(a2 / x), vary a by using a slider Cochleoids r(x) = a * sin(x) / x, vary a by using a slider Conic Sections r(x) = k * e /(1 - e * cos(x)), vary k and e by making then sliders Circles, ellipses, parabolas, and hyperbolas can be formed. This instructional construction is for students and teachers to learn how to use parametric curve command to graph polar graphs.