Richard Harrison wrote:

Roy, W7EL wrote:
"When asked for the justification of the "cosine rule", he never offered
any, so its origin remains obscure."

It comes from the similarity of a standing wave antenna to a
transmission line. It isn`t a prominent feature of antenna texts because
energy isn`t confined to an antenna as it is to a transmission line.
Antenna behavior is more complicated. Terman refers the reader to his
transmission line section to explain standing wave antenna action
innstead of making a detailled explanation in his antenna section. Maybe
he was limited in number of pages. The explanation is available from a
collection of sources.

From "Transmission Lines, Antennas, and Wave Guides" by King, Mimno,
and Wing, page 93:
"---the distribution of current in antennas with h=WL/4 and with a wide
range of radii can be represented quite accurately by:

Iz = Io cos beta(z)

beta(z) is the distance from the antenna input in degrees.

It is obvious that the current must reverse directions at the open
circuit end of the antenna. This results in a total of forward and
reflected current of nearly zero while 1/4-wave back from the open
circuit, a current maximum results.

Excellent. Roy is telling us that beta(z) at one end of the coil is
essentially equal to beta(z) at the other end of the coil. And Reg
might have us believe it's the length of the bobbin that matters in this
regard.

73, Jim AC6XG