Note that the cosine appears because black bodies are Lambertian (i.e. they obey Lambert's cosine law), meaning that the intensity observed along the sphere will be the actual intensity times the cosine of the zenith angle. To derive the Stefan–Boltzmann law, we must integrate d Ω Ω = sin ⁡ ⁡ θ θ d θ θ d φ φ over the half-sphere and integrate ν ν from 0 to ∞.