#!/usr/bin/python3

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

#Q2
def dottie(x): #Estimates dottie's constant with accuracy <=0.00001 with initial guess x
    while abs(np.cos(x)-x) > 0.00001:
        x = x + (np.cos(x)-x)/(np.sin(x)+1)
    return x

print(dottie(0.5))