Cos^2(2theta) 3d polar graph in MATLAB

How do i graph cos^2(2theta) in 3d ploar grpah? in MATLAB

Cos^2(2theta) where 0=<theta=<90 and 0=<phi=<360

[John D'Errico]

This is a function of ONE variable, as far as you have said. The cosine function returns a single value for any input.

How do you expect to plot that in THREE dimensions? What do you want to see?

[Tracy Colbert]

cos^2(2theta) where 0<= theta<=90 and 0<=phi<=360, im sorry im new to MATLAB

[Star Strider]

What’s phi?

[Tracy Colbert]

Literally this is all ive been given, i know it is supposed to look like a dome

[David Goodmanson]

Hello Tracy,

Assume that theta and phi have the usual convention for spherical coordinates,

x = r*sin(theta)*cos(phi)    y = r*sin(theta)*sin(phi)    z = r*cos(theta)

Then if the intent is r = constant, and new z = f(theta), it seems more likely that the function would be cos^2(theta). This will give something that is axially symmetric around the z axis and looks like the end of a football. But If the intent is r = f(theta) and z defined in the usual way, then cos^2(2*theta) works but does not look like a dome. Does any of the material you have mention the meshgrid function, or plotting using surf?

Answer 1

[Walter Roberson]

%0=<theta=<90 and 0=<phi=<360
[Theta, Phi] = meshgrid(linspace(0,90,361), linspace(0,360,361));
%cos^2(2theta)
R = cosd(2*Theta).^2;
[X, Y, Z] = sph2cart(Theta, Phi, R);
surf(X, Y, Z, 'edgecolor', 'none')
xlabel('X'); ylabel('Y')

[Tracy Colbert]

Thank you very much!!!

[Walter Roberson]

I forgot to account for degrees.

%0=<theta=<90 and 0=<phi=<360
[Theta, Phi] = meshgrid(linspace(0,90,361), linspace(0,360,361));
%cos^2(2theta)
R = cosd(2*Theta).^2;
[X, Y, Z] = sph2cart(Theta*pi/180, Phi*pi/180, R);
surf(X, Y, Z, 'edgecolor', 'none')
xlabel('X'); ylabel('Y')

Answer 2

[Harshvardhan]

% Define theta and r vectors
theta = linspace(0, 2*pi, 360);
r = cos(2*theta).^2;

% Convert polar coordinates to Cartesian coordinates
x = r.*cos(theta);
y = r.*sin(theta);
z = r;

% Plot 3D polar graph
plot3(x, y, z)
title('3D Polar Graph of cos^2(2\theta)')
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')