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A new mathematical algorithm has been developed for the tangent. The form of the equation guarantees that the error is zero at 0°, 45°, and 90° corresponding to tangents of 0, 1, and infinity. With only one constant the error is brought to zero at two more points and the maximum error is less than one part in 3000. By adding a second constant, the error is reduced to less than one in 720 000. Further terms improve the accuracy geometrically.