Polar Functions

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Polar functions are entered in terms of r and θ. Because there is no θ key on a computer keyboard, the graph tool uses th to represent θ.


You can enter a normal polar equation such as r = 5 sin 3θ by typing


r = 5 sin 3th




5 sin 3th


The r = is optional and will be assumed if you do not enter it.




the graph tool can also draw inverse Polar functions - just enter them in terms of r.


th = 3r


th = 1/r


th = pi/4




As shown above, the graph tool can draw polar grids.  Go to the Grid page and check Polar Grid




Default Domains

Cartesian and Inverse Cartesian functions have an "implied domain" - the bounds of the axes you have drawn the function on.  If you have not explicitly set a domain, the graph tool can automatically determine a suitable domain from the axes it is using.  For Polar graphs, there is not a natural domain that can be easily determined.  To counter this problem, the graph tool uses some default domains for polar graphs.


Polar graphs        0 ≤ θ ≤ 360 (degrees mode)

         0 ≤ θ ≤ 2π (radian mode)


In most cases these default domains produce acceptable results.  Sometimes you may need to override the default domains in order to create the result you are after.