Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...

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1

Graph these polar equations using Geogebra:
1)r=-pi/4
2)r=2(1-sin(θ))

It's not hard to generate polar plots in GeoGebra; but they are not native, so there is no direct support.

The technique is to define an angle, say θ, as a number/slider. In the input field type θ = pi, enter. Open the properties of θ and change starting value to 0, ending value to 2 pi, and animation to Increasing. Show the slider.

Type r = (some expression) in input field; enter.

Type P = (r cos(θ), r sin(θ)) in input field; enter.

Find Locus tool (4th tool in tool-bar, last item in list), click to select it, then click on P then on θ. A graph will appear of all possible locations of P for any value of the θ slider.

To see where the point is at any particular value of θ simply drag the slider. To watch it automatically go through all values, turn on animation of θ.

I drew both equations on the same plane. r = pi/4 is the circle; it has constant radius for all theta angles. r = pi/4 is sort-of the polar equivalent to y = pi/4. In both cases the value is the same for ANY value of the independent variable (theta and x, respectively).

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