Graph of polar equation

Drawing the graph of a polar equation

We deal with a folium r = sin (nθ) as an example.

• At first, select an object P (others are also available) in the Curve Area and also select the polar function as a function type.
• Input "r = sin nθ".
  To input "θ" on the calculator, input "@".
• Set the increment.
  This determines how "dotted" the graph will look like on the screen.
• Set the range if you wish.
• Set the color and the thickness of curve and point.
• Click [OK]
  
  

Negative radius

In the polar equation r = f (θ), the radius r can sometimes be negative. In that case, we can preceed in two ways:

1. There is no such a point;
   
2. Take (r, θ), r < 0, to be (-r, θ + π).
   

GRAPES adopts the second way by default. But you can modify the setting as necessary. To modify it, on the Data panel [Option | Graph Options] or in the [Option] on the [Graph] palette, set [Not Allowed] at [Negative Radius].

Drawing the graph of an relation with r and θ

• By inputting an relation with an expression using r and θ, you can draw the graph of the polar equation.
  • You can use x and y in an expression at the same time.
  • Because the parameter θ is dealt with as an argument in the relation, θ in the relation cannot be substituted by a value.
  • The graph will not be sometimes correctly drawn, if the funcion has discontinuities.

[The hot skinny of GRAPES]

r = Sqrt (x² + x²), θ = arg (x, y). "arg" is a function which gives an argument and takes a value from 0 to 2π or from -π to π. Because of this, when a point (x, y) moves across the x axis, the value of arg (x, y) changes discontinously and the graph of function will not be sometimes correctly drawn.