  The rate of extensive air-showers observed with imaging air-Cherenkov
telescopes is zenith angle dependent. This effect originates from the
increasing geometrical distance of the observed shower to the telescope with
increasing zenith distance. This paper investigates how this alters the
observed image and how this affects the trigger rate as a function of zenith
angle. The discussed effects include the change of Cherenkov light yield, of
absorption in the atmosphere, of photon density at the aperture and of the
image size at the focal plane of the telescope. Based on a simple model for the
atmosphere and well-known first principles on the development of extensive
air-showers, the zenith angle dependence is expressed analytically. The
assumption that most light is emitted from the shower core and mathematical
approximations allow to derive an analytical expression describing the zenith
angle dependence well with only three free parameters which are directly linked
with the underlying physics. This suggests further investigations about how
these fit parameters are linked to the properties of the atmosphere and the
instrument. Using data published by the First G-APD Cherenkov Telescope, a good
match of the fit functions with the data is obtained. For the trigger rate of
cosmic rays, the obtained parameters are consistent with the naive expectation.

Instrumentation and Methods for Astrophysics