# Solving Equations in MATLAB

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trythisone noone on 27 Dec 2020
Commented: Ameer Hamza on 28 Dec 2020
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?

Ameer Hamza on 27 Dec 2020
Edited: Ameer Hamza on 27 Dec 2020
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)
##### 2 CommentsShowHide 1 older comment
Ameer Hamza on 28 Dec 2020
I am glad to be of help!

John D'Errico on 27 Dec 2020
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.

R2018a

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