Providing actual values should have resolved any latent ambiguity.
Nevertheless, I should have assumed the use of a TI calculator.

Beta-sub-N = ArcSin( (N * 74.948)/(H * F))

The argument of the ArcSin is the product of N times the indicated
coefficient all divided by the product of the height times the frequency.

Height is in meters. Frequency is in MHz. N is an integer. Even values of
N apply to nulls. Odd values of N apply to peaks. Beta-sub-N is an angle
in degrees measured from the horizon towards the zenith.

The equation assumes an isotropic*, purely horizontally polarized antenna;
and a ground that is flat and has a reflection coefficient of minus-one for
an incident horizontally polarized wave independent of the
angle-of-incidence.

* Note: In this context, isotropic is to be understood to mean broadside
gain is constant and is independent of angle.

Fortunately, broadside to most horizontally antennas and for most
grounds, the conditions are close to being satisfied for Beta up to perhaps
30 degrees. The angles that are important for "DX," I have found to be
between two and twelve degrees. In other words, if long distance contacts
are desired, it is desirable to have most of an antenna's gain be between 2
and 12 degrees above the horizon.

Consider the person who places a 14.2 MHz Yagi at 60 meters (the magic
height above which one has to deal with the FAA). As a first approximation,
such an antenna is expected to have a peak at about 5 degrees and a null at
about 10 degrees. When the band opens, such a system is likely to dominate.
When propagation is better, those with lower antennas might have more gain
at the useful angle.

73 Mac N8TT
--
J. Mc Laughlin; Michigan U.S.A.
Home:
"Reg Edwards" wrote in message
...

"J. Mc Laughlin" wrote

Beta-N = ArcSin(N * 74.948/H * F)

=========================

There are two typing errors in the above equation.

Beta-N does not mean Beta minus N.
It just means the N'th value of Beta.

And the intended equation should be -

Beta = ArcSin(74.948*N/H/F) degrees.

Alternatively,

Sin(Beta) = 74.948*N/H/F degrees.

That is, divide by F, NOT multiply by F.
----
Reg, G4FGQ