import numpy as np

class Point:
    def __init__(self, x, y):
        self.x, self.y = x, y

    def __str__(self):
        return f'({self.x:g}, {self.y:g})'

class PolarPoint(Point):
    def __init__(self, r, theta):
        self.r = r
        self.theta = theta
        super().__init__(r * np.cos(theta), r * np.sin(theta))

    def __str__(self):
        return super().__str__() + f'({self.r:g}, {self.theta:g})'


def test_PolarPoint():
    """
    r, theta = (1, pi/2) -> x,y = (0,1)
    """
    tol = 1e-10
    pp = PolarPoint(1, np.pi/2)
    max_error = max(abs(pp.r - 1), abs(pp.theta - np.pi/2), abs(pp.x), abs(pp.y -1)) 
    assert max_error < tol

test_PolarPoint()





pp = PolarPoint(1.0, np.pi/4)
print(pp)