Plotting Spherical Coordinates

Question

I'm trying to plot the Poisson Kernel, where a = 1, so the resulting equation would be $$P(r,\theta) = \frac{1-r^2}{1-2r\cos(\theta)+r^2}$$ $0\leq r <a = 1 ,\textrm{ } -\pi \leq \theta \leq \pi$

I'm really having trouble visualizing what this function looks like and how to plot it by hand(without using any mathematical software)

Answer 1

Use SageMath. You can see the plot there.