import matplotlib.pyplot as plt
import numpy as np

# use latex
plt.rc('text', usetex=True)
plt.rc('font', family='serif')

x = np.linspace(0, 2 * np.pi, 100)

plt.subplot(411)
y11 = np.sin(x) * 3
y12 = np.sin(4*x)
y1 = y11 + y12
plt.plot(x, y11, label=r"$3\sin(x)$")
plt.plot(x, y12, label=r"$\sin(4x)$")
plt.plot(x, y1,  label=r"$3\sin(x) + \sin(4x)$")
plt.title("Zero Phase")
plt.legend()

plt.subplot(412)
y21 = np.sin(0.3 + x) * 3
y22 = np.sin(0.3 + 4*x)
y2 = y21 + y22
plt.plot(x, y21, label=r"$3\sin(x+0.3)$")
plt.plot(x, y22, label=r"$\sin(4x+0.3)$")
plt.plot(x, y2 , label=r"$3\sin(x+0.3) + \sin(4x+0.3)$")
plt.title("Phase = 0.3")
plt.legend()

plt.subplot(413)
y31 = np.sin(0.3*1 + x) * 3
y32 = np.sin(0.3*4 + 4*x)
y3 = y31 + y32
plt.plot(x, y31, label=r"$3\sin(x+0.3)$")
plt.plot(x, y32, label=r"$\sin(4x+0.3*4)$")
plt.plot(x, y3 , label=r"$3\sin(x+0.3) + \sin(4x+0.3*4)$")
plt.title("Phase = 0.3$\omega$")
plt.legend()

plt.subplot(414)
plt.plot(x, y1, label='Zero Phase')
plt.plot(x, y2, label='Phase = 0.3')
plt.plot(x, y3, label='Phase = 0.3$\omega$')
plt.title("Compare three function above")
plt.legend()

plt.show()