from drawtool import DrawTool
import random
import math

dt = DrawTool()
# Notice: x ranges between 0 and 3.141, y ranges between 0 and 1.
dt.set_XY_range(0,3.141, 0,1)
dt.set_aspect('equal')

random.seed(123)

# This draws the sin function.
x = 0
m = 100
interval = 3.141/m
dt.set_color('k')
for i in range(m):
    y = math.sin(x)
    dt.draw_point(x,y)
    x += interval


# Generate n=1000 random points.
n = 1000
# Count how many of them have their y value below sin(x)
count = 0

# Write your code here



print('area estimate =', (count/n)*3.141)
print('what theory predicts:', 2)

dt.display()