The task is to compute a (3,4)-Padé approximant for $sin(x)$, that is, two rationals polynomials $r,t$ with $\deg r < 3, \deg t \leq 4$ such that t has a nonzero constant coefficient and $r/t \equiv T_7 \mod{x^{3+4}}$ where $T_7$ is the dregee 7 Taylor polynomial of $sin(x)$ with center 0.
Well, I computed $T_7=x-x^3/6+x^5/120-x^7/5040$. However, I'm stuck on proceeding with this task.