smmc-2022_A3

import numpy as np
import matplotlib.pyplot as plt

# Define the functions f(x) and g(x)
def f(x):
    return np.sin((np.pi * np.sin((np.pi * x) / 2)) / 2)

def g(x):
    return (2 / np.pi) * np.arcsin((2 / np.pi) * np.arcsin(x))

# Define the interval and compute the values
x_vals = np.linspace(0, 1, 400)

# Plot the functions
plt.figure(figsize=(10, 6))
plt.plot(x_vals, [f(x) for x in x_vals], label='$f(x)$')
plt.plot(x_vals, [g(x) for x in x_vals], label='$g(x)$')
plt.plot([0, 1], [0, 1], linestyle=':', color='gray', label='$y=x$')

plt.title('Graphs of $f(x)$ and $g(x)$')
plt.xlabel('$x$')
plt.ylabel('Function values')
plt.legend()
plt.grid(True)
plt.show()