CoCalc -- assignment1.ipynb

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ubuntu2204

Kernel: Octave 8.2

To start this question, first execute the following code cell

In [9]:

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 $(x_0, y_0) = (1,-3)$ .

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

Label the axes with $x$ and $y$

Include comments explaining what each line of the code does.

In [14]:

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;

Out[14]:

Repeat the plots above, but plotting only the left half of the circles.

In [17]:

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;

Out[17]:

Product

Resources

Company