# Need help with some antenna maths

Discussion in 'Hobby Electronics' started by PèéJäy, Oct 23, 2003.

1. ### PèéJäyGuest

Hi all,

Could some kind soul point me in the right direction to solve or simplify
the following:

S = a ( cos(3pi/2 cos(x)) / sinx )^2

Need to solve for x. We never learnt this in maths and none of my books seem
to cover it either. It's in relation to finding the direction of maximum

Thanks!
P.j

2. ### budgieGuest

geez, it's so long since I did that sort of trig that I'd get a sore

3. ### PèéJäyGuest

Yes, it's one of those flower shaped patterns, but unfortunately I need to
be able to prove that it's at exactly 42 and 137 degrees. I've never had to
deal with embedded trig functions yet!

4. ### The real AndyGuest

Gee, I thought I was real stupid after seeing that calculus test, but
surprisingly, I do remember this stuff. I would give the answer too, but I
am afraid I would be doing someone elses homework. I suggest heading to the
local tech bookstore and investigating schaum!! Gee he musta' been smart...

5. ### Roger LascellesGuest

If you like, you can use a spreadsheet. Fill a column with angles from 0 to
90 degrees in one degree steps. Copy the formula into the cells all the way
down the next row.

Now insert a graph into the spreadsheet which plots your two columns X,Y.
You can even make it a polar plot to get a nice radiation pattern.

This isn't "real" maths, but it tells you what you want to know.

Roger

6. ### Phil AllisonGuest

"PèéJäy"

** Seems you have your function in its simplest form - now you just
evaluate it.

To find maxima one uses differentiation - that is not solving.

............. Phil

7. ### VerminGuest

I managed to stumble through the EW quiz you posted Phil, but this has
me stymied. It would take me an afternoon to work it out even if I
could be bothered dragging out my old maths text books.

But... just from looking at it, isn't it going to be maximum as x
approaches 0?

As sin(0)=0 so as x and therefore the denominator in the above
equation approaches 0 the expression approaches infinity.

8. ### Peter MartinGuest

One way is to use Excel.

Type the function in a cell. Define x as another cell. Make a guess for x.

Then use "Goal Seek" to solve for x. If there's more than one solution
you'll need to have different starting guesses.