I want b value only but unrecognizied value are variable b ..B can be find only through trail and error with out any intiate value of b ??

p = 0:15;

% Define the constants
r = 1.4;
m = 1.6;


% Loop through each value of p
for i = 1:length(p)
    % Define the function to be solved
    tan(p(i))= 2*cot(b)*((m^2*sin(b).^2 - 1)/(m^2*(r+cos(2*b)) + 2));
    
end

Unrecognized function or variable 'b'.

% Display the results
disp(['The values of b for different values of p are:']);
disp(b);

[Dyuman Joshi]

"=" is used for assigning.

In this line of code -

tan(p(i))= 2*cot(b)*((m^2*sin(b).^2 - 1)/(m^2*(r+cos(2*b)) + 2));

you are trying to store an expression in a variable named tan. Which leads to another point that it is not a good idea to use built-in functions as variables.

If you want to solve equations numerically, a general idea is to define anonymous functions and use a solver such as fzero.

The equation might have multiple solutions for different values of p, then which solution values should be stored?

[Torsten]

Is p in degrees ? In this case, you have to use "tand" instead of "tan".

Answer 1

[Walter Roberson]

There are multiple solutions for some of the p values. The other p values lead to expressions in 6th roots of a complex polynomial.

p = sym(0:15)

p = 

% Define the constants
r = sym(1.4)

r = 

m = sym(1.6)

m = 

syms b
% Loop through each value of p
for i = 1:length(p)
    % Define the function to be solved
    sol{i} = solve(tan(p(i)) == 2*cot(b)*((m^2*sin(b).^2 - 1)/(m^2*(r+cos(2*b)) + 2)));
end


% Display the results
disp(['The values of b for different values of p are:']);

The values of b for different values of p are:

celldisp(sol)

 
sol{1} =
 

 
 
sol{2} =
 

 
 
sol{3} =
 

 
 
sol{4} =
 

 
 
sol{5} =
 

 
 
sol{6} =
 

 
 
sol{7} =
 

 
 
sol{8} =
 

 
 
sol{9} =
 

 
 
sol{10} =
 

 
 
sol{11} =
 

 
 
sol{12} =
 

 
 
sol{13} =
 

 
 
sol{14} =
 

 
 
sol{15} =
 

 
 
sol{16} =
 

celldisp(cellfun(@double, sol, 'uniform', 0))

 
ans{1} =
 
    1.5708
   -0.6751
    0.6751

 
 
ans{2} =
 
  -1.7814 + 0.6341i

 
 
ans{3} =
 
  -1.4109 + 0.6670i

 
 
ans{4} =
 
   -2.5895

 
 
ans{5} =
 
  -1.8300 + 0.5896i

 
 
ans{6} =
 
  -1.4629 + 0.6898i

 
 
ans{7} =
 
  -1.1539 + 0.1396i

 
 
ans{8} =
 
  -1.8758 + 0.5312i

 
 
ans{9} =
 
  -1.5158 + 0.7033i

 
 
ans{10} =
 
  -1.1842 + 0.3388i

 
 
ans{11} =
 
  -1.9180 + 0.4540i

 
 
ans{12} =
 
  -1.5691 + 0.7079i

 
 
ans{13} =
 
  -1.2211 + 0.4484i

 
 
ans{14} =
 
  -1.9553 + 0.3470i

 
 
ans{15} =
 
  -1.6225 + 0.7038i

 
 
ans{16} =
 
  -1.2630 + 0.5269i

 

[Walter Roberson]

Numeric solution is a bit different...

p = sym(0:15)

p = 

% Define the constants
r = sym(1.4)

r = 

m = sym(1.6)

m = 

syms b
% Loop through each value of p
for i = 1:length(p)
    % Define the function to be solved
    sol(i) = vpasolve(tan(p(i)) == 2*cot(b)*((m^2*sin(b).^2 - 1)/(m^2*(r+cos(2*b)) + 2)), 1);
end


% Display the results
disp(['The values of b for different values of p are:']);

The values of b for different values of p are:

disp(sol.')

    fplot(-tan(p(i)) + 2*cot(b)*((m^2*sin(b).^2 - 1)/(m^2*(r+cos(2*b)) + 2)), [-50 50]);
    ylim([-0.5 2])

The plot is for the last value of p(i) so it looks like there is likely an infinite number of solutions. I'm not sure why solve() only finds one.

[Walter Roberson]

Ah, once more solve() was choosing a single "representative" answer.

If you look at the conditions display for the entries after the first, you wills see several parts with multiple z1 == parts joined by v . Those v are "or" symbols -- so there are several matching numeric values for each output for the second and later solutions.

p = sym(0:15)

p = 

% Define the constants
r = sym(1.4)

r = 

m = sym(1.6)

m = 

syms b
% Loop through each value of p
for i = 1:length(p)
    % Define the function to be solved
    sol{i} = solve(tan(p(i)) == 2*cot(b)*((m^2*sin(b).^2 - 1)/(m^2*(r+cos(2*b)) + 2)), 'returnconditions', true);
end


% Display the results
disp(['The values of b for different values of p are:']);

The values of b for different values of p are:

celldisp(sol)

 
sol{1} =
 
             b: [3×1 sym]
    parameters: k
    conditions: [3×1 sym]

 
 
sol{2} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(2i))/5 - 157/80) + z^2*((157*exp(2i))/80 - 7/5) + exp(2i), z, 1) | z1 == root(z^6 - z^4*((7*e…

 
 
sol{3} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(4i))/5 - 157/80) + z^2*((157*exp(4i))/80 - 7/5) + exp(4i), z, 1) | z1 == root(z^6 - z^4*((7*e…

 
 
sol{4} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(6i))/5 - 157/80) + z^2*((157*exp(6i))/80 - 7/5) + exp(6i), z, 1) | z1 == root(z^6 - z^4*((7*e…

 
 
sol{5} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(8i))/5 - 157/80) + z^2*((157*exp(8i))/80 - 7/5) + exp(8i), z, 1) | z1 == root(z^6 - z^4*((7*e…

 
 
sol{6} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(10i))/5 - 157/80) + z^2*((157*exp(10i))/80 - 7/5) + exp(10i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{7} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(12i))/5 - 157/80) + z^2*((157*exp(12i))/80 - 7/5) + exp(12i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{8} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(14i))/5 - 157/80) + z^2*((157*exp(14i))/80 - 7/5) + exp(14i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{9} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(16i))/5 - 157/80) + z^2*((157*exp(16i))/80 - 7/5) + exp(16i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{10} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(18i))/5 - 157/80) + z^2*((157*exp(18i))/80 - 7/5) + exp(18i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{11} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(20i))/5 - 157/80) + z^2*((157*exp(20i))/80 - 7/5) + exp(20i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{12} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(22i))/5 - 157/80) + z^2*((157*exp(22i))/80 - 7/5) + exp(22i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{13} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(24i))/5 - 157/80) + z^2*((157*exp(24i))/80 - 7/5) + exp(24i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{14} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(26i))/5 - 157/80) + z^2*((157*exp(26i))/80 - 7/5) + exp(26i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{15} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(28i))/5 - 157/80) + z^2*((157*exp(28i))/80 - 7/5) + exp(28i), z, 1) | z1 == root(z^6 - z^4*((…

 
 
sol{16} =
 
             b: 2*pi*k - log(z1)*1i
    parameters: [k    z1]
    conditions: in(k, 'integer') & cos(log(z1)*2i - 4*pi*k) ~= -349/160 & (z1 == root(z^6 - z^4*((7*exp(30i))/5 - 157/80) + z^2*((157*exp(30i))/80 - 7/5) + exp(30i), z, 1) | z1 == root(z^6 - z^4*((…

 

celldisp(cellfun(@(S)vpa(S.b), sol, 'uniform', 0))

 
ans{1} =
 

 
 
ans{2} =
 

 
 
ans{3} =
 

 
 
ans{4} =
 

 
 
ans{5} =
 

 
 
ans{6} =
 

 
 
ans{7} =
 

 
 
ans{8} =
 

 
 
ans{9} =
 

 
 
ans{10} =
 

 
 
ans{11} =
 

 
 
ans{12} =
 

 
 
ans{13} =
 

 
 
ans{14} =
 

 
 
ans{15} =
 

 
 
ans{16} =
 

celldisp(cellfun(@(S)vpa(S.conditions), sol, 'uniform', 0))

 
ans{1} =
 

 
 
ans{2} =
 

 
 
ans{3} =
 

 
 
ans{4} =
 

 
 
ans{5} =
 

 
 
ans{6} =
 

 
 
ans{7} =
 

 
 
ans{8} =
 

 
 
ans{9} =
 

 
 
ans{10} =
 

 
 
ans{11} =
 

 
 
ans{12} =
 

 
 
ans{13} =
 

 
 
ans{14} =
 

 
 
ans{15} =
 

 
 
ans{16} =