Solving Equations in MATLAB

Hello,

I have the following equation.

cos(x) == 0

I want to get two or more possible solutions for the above equation which are 90, 270, and so on. The solve function returns the first solution only.

This technique is important for me to calculate the antenna beamwidths. Any ideas?

Thanks in Adv

Answer 1

[Ameer Hamza]

There is no general solution to such a problem. A common way is to specify several starting points for the numerical solver and find the unique solutions.

y = @(x) cos(x);

x_range = 0:0.1:4*pi;
y_sol = zeros(size(x_range));
for i = 1:numel(x_range)
    y_sol(i) = fzero(y, x_range(i));
end

y_sol = uniquetol(y_sol)

[trythisone noone]

Wow, Nice trick man. It works fine. <3

[Ameer Hamza]

I am glad to be of help!

Answer 2

[John D'Errico]

SOME problems can be handled to find all solutions.

syms x
>> xsol = solve(cos(x) == 0,'returnconditions',true)
xsol = 
  struct with fields:

             x: [1×1 sym]
    parameters: [1×1 sym]
    conditions: [1×1 sym]
    
>> xsol.parameters
ans =
k

>> xsol.conditions
ans =
in(k, 'integer')

>> xsol.x
ans =
pi/2 + pi*k

So we learn the set of all solutions takes the form

x = pi/2 + pi*k

where k is an integer.

Sadly, a fully general solution to many problems will not be written so easily. But you can always try.