The calculation of coupling coefficients for muon telescopes has previously used interpolation from a limited set of asymptotic directions of arrival of primary particles. Furthermore, these calculations have not incorporated curvature of the atmosphere and thus diverge from the true response at zenith angles greater than about 75 degrees. The necessary extensions to calculate coupling coefficients at arbitrary zenith angles are given, including an improved method of incorporating the asymptotic directions of the primary particles. It is shown, using this method, that certain coupling coefficients are highly sensitive to small changes in asymptotic directions for some telescope configurations. 10 refs., 1 fig., 3 tabs.