how to set a while loop in matlab

I had studied Python but I have no idea how to enter variable and set up a loop in Matlab. I need it for my final project. Please help me out. This is problem:

Each team needs to turn in a report that contains a description of your strategy/algorithm along with a MATLAB script that can be tested.  Use MATLAB to plot the equations on the x-y coordinates.  All solutions need to reach accuracy of 10-4

Find all solution of this equation: x^2 + y^2 = 0 y = tanx

Answer 1

[BhaTTa]

@Huy Ngo, to solve the system of equations (x^2 + y^2 = 0) and (y = \tan(x)) in MATLAB, we need to find the intersection points of these equations. The first equation implies that both (x) and (y) must be zero, since the sum of their squares is zero. The second equation, (y = \tan(x)), is a trigonometric function that repeats periodically.

Here's a step-by-step guide on how you can set up a MATLAB script to find and plot these solutions:

1. Define the Equations: We will use anonymous functions to define the equations.
2. Set Up a Loop: We will use a loop to evaluate the equations over a range of (x) values.
3. Plot the Equations: Use MATLAB's plotting functions to visualize the solutions.
4. Check for Solutions: Since (x^2 + y^2 = 0) implies (x = 0) and (y = 0), we will check these conditions.

Here's a MATLAB script that achieves this:

% Define the range for x

x = linspace(-2*pi, 2*pi, 1000); % Evaluate from -2*pi to 2*pi

% Define the equations

y1 = tan(x); % y = tan(x)

y2 = sqrt(0 - x.^2); % y = sqrt(0 - x^2) which is 0 since x^2 + y^2 = 0 implies y = 0

% Plot the equations

figure;

plot(x, y1, 'r', 'DisplayName', 'y = tan(x)');

hold on;

plot(x, y2, 'b', 'DisplayName', 'x^2 + y^2 = 0');

plot(x, -y2, 'b'); % Plot the negative part of y2 for completeness

hold off;

% Set plot properties

xlabel('x');

ylabel('y');

title('Plot of y = tan(x) and x^2 + y^2 = 0');

legend show;

grid on;

% Find solutions

tolerance = 1e-4;

solutions = [];

for i = 1:length(x)

if abs(x(i)) < tolerance && abs(y1(i)) < tolerance

solutions = [solutions; x(i), y1(i)];

end

end

% Display solutions

disp('Solutions found:');

disp(solutions);