On the dimension of angles and their units

Abstract

We examine implications of angles having their own dimension, in the same sense as do lengths, masses, {\it etc.} The conventional practice in scientific applications involving trigonometric or exponential functions of angles is to assume that the argument is the numerical part of the angle when expressed in units of radians. It is also assumed that the functions are the corresponding radian-based versions. These (usually unstated) assumptions generally allow one to treat angles as if they had no dimension and no units, an approach that sometimes leads to serious difficulties. Here we consider arbitrary units for angles and the corresponding generalizations of the trigonometric and exponential functions. Such generalizations make the functions complete, that is, independent of any particular choice of unit for angles. They also provide a consistent framework for including angle units in computer algebra programs.

27 pages, 2 figures, editorial changes, references added. Submitted to Metrologia

References in corpus (4)

• Dimensionless Units in the SI
• The role of unit systems in expressing and testing the laws of nature
• Angles in the SI: treating the radian as an independent, unhidden unit does not require the redefinition of the term frequency or the unit hertz
• Angles in the SI: a detailed proposal for solving the problem