import math
import numpy as np
import matplotlib.pyplot as plt

def circle_square(external_radius,inner_radius):
        return math.pi*(external_radius*external_radius-inner_radius*inner_radius)


def main():
    print(f"circle square(10,5): {circle_square(10,5)}")
    x_coords = [-3.14+i*0.02 for i in range(0, 315)]
    function1_y_coords = [2*math.sin(x_coord) for x_coord in x_coords]
    function2_y_coords = [math.cos(2*x_coord) for x_coord in x_coords]
    min_delta = 10.0
    min_coord = -1
    for index in range(0, len(x_coords)):
        current_res = abs(function1_y_coords[index]-function2_y_coords[index])
        if min_delta > current_res:
            min_delta = current_res
            min_coord = index
    print(f"intersect in (x={min_coord*0.02-3.14},y={min_delta})")
    plt.title("y1 = 2sin(x), y2 = cos(2x)")
    plt.xlabel("x")
    plt.ylabel("y1, y2")
    plt.grid()
    plt.plot(x_coords, function1_y_coords,x_coords, function2_y_coords)
    plt.show()

main()