Newton Raphson equation trig functions

Trying to calculate root to an equation using newton raphson. also need to tabulate the results. the table isn't showing any info though.

clc
clear all
syms x

T = [];  % Define table
x0 = .1;    % Define Initial Value
i = 1;      % Define Counter
N = 10;     % Define max number of iterations

% Define Variables
S = 5281.716;
L = 5280;

f(x) = x - (S/L) * sin(x);  % Define Function
df = diff(f);               % Differential Function

while i <= N

      x = x0 - (f(x0)/df(x0));    % Newton-Raphson Equation
      if abs(x-x0) <= 10^-8
          return
      end
      R = S/(2*x0);        % Radius
      d = R*(1-cos(x0));   % Distance d
      T = [T; i x0 R d];
      i = i + 1;          % Increase Counter
      x0 = x;             % Update value of x0
      vpa(x0)             % Decimal
  end
  T = table(Iteration, Theta, Radius, d);

[John D'Errico]

Homework? If not, then USE FZERO!

[Derek Reitnouer]

have to use newton raphson method. problem is haven't used matlab in years.

[John D'Errico]

You still have not answered my question. Is this homework? That is the only possible reason why you NEED to use Newton/Raphson, so the conclusion seems clear.

[Derek Reitnouer]

yes its a homework problem. I get the correct answer but can't figure out how to do the table and keep the answer to decimals.

[Muhammad Qasim]

cos(x)+2sin(x)+x^2

Answer 1

[James Tursa]

Instead of doing all of this as symbolic, it would probably have been simpler to use function handles and work in double. That being said, maybe just convert your stuff to double as you accumulate it:

T = [T; double([i x0 R d])];

Then you can use T to plot stuff directly.

Also, it would make more programming sense to change that "return" statement to a "break" statement.

[Derek Reitnouer]

I looked up the difference between return and break, thanks for the tip. I also looked at double and that makes sense. I want to name the columns on the table but it doesn't like this. Why?

clc clear all syms f(x)

T = []; % Define table x0 = .1; % Define Initial Value i = 1; % Define Counter N = 10; % Define max number of iterations

% Define Variables S = 5281.716; L = 5280;

f(x) = x - (S/L) * sin(x); % Define Function df = diff(f); % Differential Function

while i <= N x = x0 - (f(x0)/df(x0)); % Newton-Raphson Equation if abs(x-x0) <= 10^-8 break end R = vpa(S/(2*x)); % Radius d = vpa(R*(1-cos(x))) % Distance d T = [T; double([i x R d])] i = i + 1; % Increase Counter x0 = x; % Update value of x0 vpa(x0) % Decimal end T = table(Iteration, Theta, Radius, d);

Answer 2

[Derek Reitnouer]

T.Properties.VariableUnits = {'Iteration' 'Theta' 'Radius' 'd'}; T

That doesn't work either.