Here's a quote from Kraus' "Antennas For All Applications"
3rd Edition, page 177, section 6-4:

"The Thin Linear Antenna - In this section
expressions for the far-field patterns of thin linear
antennas will be developed. It is assumed that the antennas
are symmetrically fed at the center by a balanced two-wire
transmission line. The antennas may be of any length, but
it is assumed that the current distribution is SINUSOIDAL.
Current-distribution measurements indicate that this is a GOOD
ASSUMPTION provided that the antenna is thin, i.e., when the
conductor diameter is less than, say, lamda/100. Thus, the
sinusoidal current distribution approximates the natural
distribution on thin antennas." Emphasis mine.

So Kraus gives us permission to treat the currents on a
dipole as sinusoidal as long as the diameter of the element
is less than 4 inches on 30 MHz or less than 40 inches on
3 MHz. So virtually all HF dipoles are thin-wire antennas.

And since the current distribution is assumed sinusoidal, the
arc-cosine function will yield the number of degrees a point
is away from a current maximum point, e.g. the phase information
for the forward traveling wave.
--
73, Cecil, http://www.qsl.net/w5dxp