The black hole binary Cygnus X-1 was observed in late-2012 with the Nuclear Spectroscopic Telescope Array (NuSTAR) and Suzaku, providing spectral coverage over the ~1-300 keV range. The source was in the soft state with a multi-temperature blackbody, power-law, and reflection components along with absorption from highly ionized material in the system. The high throughput of NuSTAR allows for a very high quality measurement of the complex iron line region as well as the rest of the reflection component. The iron line is clearly broadened and is well-described by a relativistic blurring model, providing an opportunity to constrain the black hole spin. Although the spin constraint depends somewhat on which continuum model is used, we obtain a*>0.83 for all models that provide a good description of the spectrum. However, none of our spectral fits give a disk inclination that is consistent with the most recently reported binary values for Cyg X-1. This may indicate that there is a >13 degree misalignment between the orbital plane and the inner accretion disk (i.e., a warped accretion disk) or that there is missing physics in the spectral models.
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