from math import sin,tan,pi

def f(x):
    return sin(x)

print 'Bisection method'
a=3.0
b=4.0

m=(a+b)/2.0
for i in range(1,11):
    if f(m)==0:
        a=b=m
    if f(a)*f(m)<0:
        b=m
    else:
        a=m
    m=(a+b)/2.0
    print i,m,(m-pi)/pi

print 'Secant method'
xpp=4.0
xp=3.0
for i in range(1,5):
    z=xp-f(xp)*(xp-xpp)/(f(xp)-f(xpp))
    xpp=xp
    xp=z
    print i,xp,(xp-pi)/pi

print 'Newton method'
x=3.0
for i in range(1,5):
    x=x-tan(x)
    print i,x,(x-pi)/pi