Given that

    Σm = 1 to 44 cos mo
y = ---------------
    Σm = 1 to 44 sin mo


Find the value of floor(100y)

By regrouping the terms of the numerator we get: 

Σ_{m = 1 to 44} cos m  =(2*cos(45/2)) *(cos(43/2)+ cos(41/2)+ cos(39/2)+… cos(1/2))  (i)

By the same reasoning:

Σ_{m = 1 to 44} sin m     =(2*sin(45/2)) *(cos(43/2)+
cos(41/2)+ cos(39/2)+… cos(1/2))     (ii)

So:  y=cot (45/2 )

Since tan 45=1    and   tan 2x=2x/(1-x^2)  
  cot (22.5)=1+sqrt(2)

Answer: floor 100*(1+sqrt(2)= 241