astrometry - Transform pixel coordinates (in FITS file) to equatorial

Assuming that each (square) pixel has the same angular scale (not a given if the field of view is large) of $theta$ degrees/pixel.

Then the declination (in degrees): $delta simeq delta_0 + theta y$

The right ascension (in degrees): $alpha simeq alpha_0 - theta x/cos delta$

where $alpha_0$ and $delta_0$ are the RA and Dec at $x=0$, $y=0$. [The minus sign is there because right ascension increases towards the left of a sky image.]

This approximatimation becomes poor as the field of view gets larger.

A slightly more complex, but accurate, approach is described in http://gtn.sonoma.edu/data_reduction/astrometry.php

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