Plotting equations using SAGE

It is very handy to plot maths equations using the SAGE maths open source software.

For example, to plot a straight line:
> plot(3*x + 4, (x,0,5))

To plot a function, showing its asymptotes (requires us to set detect_poles=show):
> f = (5*x+2)/(2*x+3)
> plot(f, (x,-7,7), detect_poles='show').show(ymin=-50, ymax=50)

 To plot a function, filling in the area between the function and its asymptote:
> plot(f, -7,7, fill = {0: [1]}, fillcolor='#ccc').show(ymin=-50, ymax=50)

To plot a trigonometric function:
> plot(tan(x), (x,-20,20), detect_poles='show').show(ymin=-10, ymax=10)

  

Plotting two functions on top of each other:
>  plot(cos(x), (x,-3*pi,3*pi), color='blue') + plot(sin(x), (x,-2*pi,2*pi), color='red')

We can also plot parametric equations, for example, if x = t - sin(t), and y = 1 - cos(t), which is a cycloid curve:
> var('t')
> parametric_plot((t-sin(t),1-cos(t)),(t,0,30),rgbcolor=hue(0.6))