02 Learning Polar Graphing
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}