I know that |z| <= 1 , but is there is a more accurate estimation ?
thx
What exactly are you asking for?
z is continious on x <= |0.1|, you can say something about slope and it has the sin-symmetry. And you know z(0) = 0; there are no zeros except for x=0 on your interval...
I know that |z| <= 1 , but is there is a more accurate estimation ?
To a first approximation, z = x. If you want something more accurate, the next approximations are $\displaystyle z = x-\tfrac23x^3$ and $\displaystyle z = x-\tfrac23x^3 + \tfrac2{15}x^5$.