#!/usr/bin/env python3
# takes two columns of points as r theta pairs
# and plots them in a unit circle.
#    Author: Robert Heckendorn  for CS472 Nov 6, 2020
import sys
import numpy as np
import matplotlib.pyplot as plt

def main() :
    # collect data
    xx = []
    yy = []
    for inline in sys.stdin :
        line = inline.split()
        r = float(line[0])
        theta = float(line[1])
        x = r * np.cos(theta)
        y = r * np.sin(theta)
        xx.append(x)
        yy.append(y)

    # plot the circle
    theta = np.linspace(0, 2*np.pi, 100)
    x = np.cos(theta)
    y = np.sin(theta)
    plt.axes().set_aspect(1.0)
    plt.plot(x, y)

    # plot and save the data
    plt.scatter(xx, yy, c='#ff0000')
    plt.savefig("unit.png")

main()