Hyperspherical coordinates are well suited for treating rearrangement processes in the strong interaction region, and several different hyperspherical coordinates have been used successfully for quantum reactive scattering by various research groups. However, it is well known that asymptotically the appropriate set of coordinates (for a three particle system) are the three sets of Jacobi coordinates. In this paper we show how one can smoothly connect the hyperspherical coordinates in the rearrangement region to Jacobi coordinates in the nonrearrangement region using tangent-sphere coordinates. This procedure reduces the computational time required to solve the quantum Schrodinger equation and eliminates the need for numerical projection. To illustrate this method, we apply it to the F+H(2)reversible arrow HF+F reaction, comparing reaction probabilities to those from previous benchmark calculations based on a conventional formulation.