Circuitry for computing a trigonometric function of an input includes circuitry for relating the input to another value to generate an intermediate value, circuitry for selecting one of the input and the intermediate value as a trigonometric input value, circuitry for determining respective initial values of a plurality of trigonometric functions for the trigonometric input value, and circuitry for deriving, based at least in part on a trigonometric identity, a final value of the first trigonometric function from the respective initial values of the plurality of trigonometric functions. The trigonometric function may be any of sine, cosine and tangent and their inverse functions. The trigonometric identities used allow a computation of a trigonometric function to be broken into pieces that either are easier to perform or can be performed more accurately.