'''
Program carousel-range.py

At which angle of deflection should a physical 
pendulum released at the top be released/broken 
to achieve maximum horizontal distance from the 
pendulum's axis? How far will it fly w/o friction?

x  = max range in units of pendulum rad. R 
co = cos(theta)  <- search on uniform mesh
''' 
from numpy import sqrt,cos,pi

def rangex(co):          
    si = sqrt(1.-co*co)  # sin(theta)
    tmp = 1.+co   
    return si +2.*co  \
      * (tmp*si +sqrt(tmp*(2.-co*co*tmp))) 


theta = 1.
while (theta > 0.):
    theta = float(input(" theta[deg] = "))
    co = cos(theta/180*pi)   # cos(theta)
    print(theta,'   range/R =',rangex(co))