  The giant planet orbiting tau Bootis was among the first extrasolar planets
to be discovered through the reflex motion of its host star. It is one of the
brightest known and most nearby planets with an orbital period of just a few
days. Over the course of more than a decade, measurements of its orbital
inclination have been announced and refuted, and have subsequently remained
elusive until now. Here we report on the detection of carbon monoxide
absorption in the thermal day-side spectrum of tau Bootis b. At a spectral
resolution of R~100,000, we trace the change in the radial velocity of the
planet over a large range in phase, determining an orbital inclination of
i=44.5+-1.5 degrees and a true planet mass of 5.95+-0.28 MJup. This result
extends atmospheric characterisation to non-transiting planets. The strong
absorption signal points to an atmosphere with a temperature that is decreasing
towards higher altitudes. This is a stark contrast to the temperature inversion
invoked for other highly irradiated planets, and supports models in which the
absorbing compounds believed to cause such atmospheric inversions are destroyed
by the ultraviolet emission from the active host star.
