Minimal example:
import numpy as np
import matplotlib.pyplot as plt
x_ = np.arange(2000)
frequency = 2 * np.pi
sine = np.sin(x_*frequency)
plt.plot(x_, sine)
plt.show()
produces following plot:
The multiplication np.sin(x_*frequency) results in very confusing behavior. How can the output of the sine function be smaller than -1 and showing multiple amplitudes?
If np.sin(x_/frequency) than it shows the expected behavior:
>Solution :
You think you’re drawing a continuous function, but all the points in vector x_ are of the form (integer) * 2 pi. And the sin of a multiple of 2pi is 0.
So the points you’re giving to plt.plot are only points where the sin is 0.
They are not exactly 0, because np.pi is not exactly pi, and you’re multiplying that error by up to 2000.
What you’re observing is that the error on np.sin(2000 * 2 * np.pi) is on the order of 1e-12, or 0.000000000001 if you prefer that notation.
If you want to observe a curve that looks more like the curve of sin, try including non-integers in vector x:
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0,10,1000) # 1000 points in interval [0, 10]
y = np.sin(x * 2 * np.pi)
plt.plot(x,y)
