The conversion between spherical and Cartesian coordinates is x = r sin θ cos φ, y = r sin θ sin φ, z = r cos θ. The function Y = 3 cos^2 θ - 1 is labeled as d because cos^2 θ is proportional to z^2. Linear combinations of Ym yield the other four familiar d orbital shapes: dxy, dxz, dyz, and dz^2. Show how the angular dependence of each of these corresponds to one of the commonly used labels for these d orbitals: dxy, dxz, dyz, and dz^2. Double-angle formulas may be useful. Based on McQuarrie & Simon, 6-42.