Animated plots may help you:

https://doc.sagemath.org/html/en/reference/plotting/sage/plot/animate.html

For play button, you may use interactive(). For example,

x = SR.var("x")
sines = [plot(c*sin(x), (-2*pi,2*pi), color=Color(c,0,0), ymin=-1, ymax=1) 
for c in range(0,1,.2)]
a = animate(sines)
a.interactive()

It is unfortunate this interactive animated plot is rendered in 3d, though.



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