Equatorial to tangent plane conversion

The first step in the conversion process is to derive the standard coordinates $\xi$ and $\eta$ for the guide stars. These are given by:

$\xi =\; \{cos\delta sin(\alpha -\; \alpha$₀)sinδsinδ₀ + cosδcosδ₀cos(α- α₀)}

$\eta =\; \{sin\delta cos\delta$₀ - cosδsinδ₀ cos(α- α₀)sinδsinδ₀ + cosδcosδ₀cos(α- α₀)}