import numpy as np
import matplotlib.pyplot as plt

"""
    Plots the function
        f(x) = sin(n*x)
    over a given interval.

    Arguments:
        x : Numpy array
        n : Integer value
"""
def plot_sine(x, n):
    y = np.sin(n*x)

    plt.plot(x, y)

"""
    Plots the function
        g(x) = cos(n*x)
    over a given interval.

    Arguments:
        x : Numpy array
        n : Integer value
"""
def plot_cosine(x, n):
    y = np.cos(n*x)

    plt.plot(x, y)


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

plot_cosine(x, 0)

for n in range(1, 4):
    plot_sine(x, n)
    plot_cosine(x, n)

plt.xlim([min(x), max(x)])
plt.savefig("trigonometric_basis_0to3.svg", format="svg")
plt.show()