  In this paper we study a metric generalization of the sine function which can
be extended to arbitrary normed planes. We derive its main properties and give
also some characterizations of Radon planes. Furthermore, we prove that the
existence of an angular measure which is "well-behaving" with respect to the
sine is only possible in the Euclidean plane, and we also define some new
constants that estimate how non-Radon or non-Euclidean a normed plane can be.
Sine preserving self-mappings are studied, and a complete description of the
linear ones is given. In the last section we exhibit a version of the Law of
Sines for Radon planes.
