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Kernel: Octave 8.2

To start this question, first execute the following code cell

radii = [1, 3, 5, 9];

Using a for loop (see lab 1) and the recommended parametrization of a circle (see lab 2) plot a circle with each radius in the array radii centered at (x0,y0)=(1,−3)(x_0, y_0) = (1,-3).

Make sure all of the circles appear in the same figure and are not overwritten.

Label the axes with xx and yy

Include comments explaining what each line of the code does.

radii = [1, 3, 5, 9];

% Define the center of the circles
x0 = 1;  
y0 = -3;

% Define theta values for full circles
theta = linspace(0, 2*pi, 100);

% Create a figure
figure;
hold on; % Ensures all circles are plotted on the same figure
axis equal; % Keep aspect ratio of circles correct

% Loop through each radius in the array
for r = radii
    % Parametric equations for the circle
    x = x0 + r * cos(theta);
    y = y0 + r * sin(theta);
    
    plot(x, y, 'LineWidth', 4);
end 

% Label axes
xlabel('x');
ylabel('y');
title('Circles of Different Radii');

% Show grid
grid on;
hold off;
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Repeat the plots above, but plotting only the left half of the circles.

radii = [1, 3, 5, 9];

% Define the center of the circles
x0 = 1;  
y0 = -3;

% Define theta values for the left half-circle (π/2 to 3π/2)
theta_left = linspace(pi/2, 3*pi/2, 50);

% Create a new figure
figure;
hold on;
axis equal;

% Loop through each radius in the array
for r = radii
    % Parametric equations for the left half-circle
    x = x0 + r * cos(theta_left);
    y = y0 + r * sin(theta_left);
    
    % Plot the left half-circle
    plot(x, y, 'LineWidth', 4);
end

% Label axes
xlabel('x');
ylabel('y');
title('Left Half of Circles');

xlim([-10, 5]); 
ylim([-15, 7]);
grid on;
hold off;
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