function f = my_fun(x)
f = cos(4*x*sqrt(1-x^2))-(-1+8*x^2-8*x^4);

---------
Hint: execute

>> format long

to see more digits of numbers
---------
Execute:

>> zeta = bisection('my_fun',0,1,5e-7)
>> tau_f = acos(zeta)/sqrt(1-zeta^2)
>> tau_m = acos(zeta*(3-4*zeta^2))/sqrt(1-zeta^2)
>> F_m = exp(-zeta*(tau_f + tau_m))