how do you graph z=sqrt(9-r​^2cos^2(th​eta))?

syms x y z;

[x,y,]=meshgrid(-10:1:10);

z = abs(sqrt(9-r.^2*cos.^2(theta)));

surf (r,theta,z);

ylim([-1,2]);

xlabel('x');

ylabel('y');

zlabel('z');

[Walter Roberson]

You have not defined r or theta.

The syms is not doing anything for you there.

If you need to convert x y coordinates to polar coordinates then see cart2pol()

[Carter Pennington]

[theta,r] = cart2pol(x,y);

[theta,r]=meshgrid(-10:1:10);

z = abs(sqrt(9-r.^2*cos.^2(theta)));

surf (theta,r);

?????

Answer 1

[Aoi Midori]

z = 3 when r = 0:

[r]=meshgrid(0:0.1:6.28);
[theta]=meshgrid(0:0.1:2*pi);
z = abs( sqrt( 9 - (r.^2 .* cos(theta').^2 ) ) );
surf (r,theta',z);
xlabel('r');
ylabel('theta');
zlabel('z');

Answer 2

[Carlos Guerrero García]

I think that Carter Pennington was talking about the parametrized surface

x=r*cos(theta)

y=r*sin(theta)

z=sqrt(9-r^2*(cos(theta))^2)

with 0<=theta<=2pi and 0<=r<=3 (for real values of z)

In consecuence, I will plot the graph in the sentence with the followng lines:

[r,theta]=meshgrid(0:0.1:3,0:pi/60:2*pi); % In the supposed range
x=r.*cos(theta); % The classical definitons of the
y=r.*sin(theta); % polar coordinates for "x" and "y"
z=sqrt(9-r.^2.*(cos(theta)).^2); % The condition in the question
surf(x,y,z); % The graph
hold on; % and keep the focus on the figure for
surf(x,y,0.*x); % plotting the range in the XY plane
shading interp; % Optional for showing the mesh lines
axis equal % For an adequate view