plt.set_cmap will set a colormap to be used, for example, in an image plot. As you're simply plotting lines, it won't affect your plots.
When plotting using plt.plot you can provide a color keyword argument which will choose the color of your lines, as below.
# ...
plt.plot(x,y, color='black')
plt.plot(x,y1, color='pink')
plt.plot(x,y2, color='green')
plt.show()
Alternatively, you could set a new color cycle using the ax.set_color_cycle(), which allows you to choose how the colors will change as you add new plots and effectively creates the same graph as before. See here for a demo.
# ...
plt.gca().set_color_cycle(['black', 'pink', 'green'])
plt.plot(x,y)
plt.plot(x,y1)
plt.plot(x,y2)
plt.show()
Finally, if you want to get a list of colors from an existing colormap then you can use the below code to get them spaced out linearly. The colormap itself is given by matplotlib.pyplot.cm.<your_colormap_here>. And by passing 10 equally spaced numbers between 0 and 1 as an argument, you get 10 equally spaced colors.
import numpy as np
import matplotlib.pyplot as plt
x=np.linspace(-np.pi,np.pi,101)
y=np.sin(x)+np.sin(3*x)/3
y1=np.sin(x)+np.sin(2*x)/3
y2=np.sin(x)+np.sin(3*x)/2
colors = plt.cm.hot(np.linspace(0,1,10))
plt.gca().set_color_cycle(colors)
plt.plot(x,y)
plt.plot(x,y1)
plt.plot(x,y2)
plt.show()
