On the Trigonometric Relation between Tax Audit and Underreporting Rates

The probabilities associated with a tax return being audited or containing underreported tax are formulated here in a different way. This new formulation is mathematically equivalent to the traditional formulation; however, it reveals a trigonometric relationship between these probabilities that cannot be deduced from the familiar approach. Unconditioned probabilities associated with audits and underreporting are expressed as the square of the magnitudes of probability amplitude vectors. Conditioned probabilities are expressed as the square of trigonometric functions (cosine or sine) of the angle between probability amplitude vectors and the axes of two-dimensional coordinate systems. Although applications are not discussed, this new way of considering tax audit and underreporting rates will hopefully inspire others to find solutions to problems otherwise thought unsolvable