MATLAB: Graph of y = 1 / ( cos(x) -c)

MATLABplot graph

i am trying to plot a graph of y = 1 / ( cos(x) -c) where c comes from initial conditions.

When I do a graph by hand for each of the initial conditions I get plots above and below the axis but all my matlab plots are below zero.

C = cos(c) – 1/y

When I hard code the values for C the graph works fine so I expect it is these lines of code.

if true
x0 = [0 pi/2 pi/2 pi/2 pi/2 pi/2 pi/2]
y0 = [1 -1/2 1/2 -2/3 2/3 -1 1]   
C = cos(x0) - (1./y0);
for C= 1:7
end
if true
  % code
hold on
grid on
x=[0: pi/20: 4*pi]
axis([0 4*pi -5 1])
x0 = [0 pi/2 pi/2 pi/2 pi/2 pi/2 pi/2]
y0 = [1 -1/2 1/2 -2/3 2/3 -1 1]   
C = cos(x0) - (1./y0);
for C= 1:7
y = 1./(cos(x) -C);
plot (x,y,'color',rand(1,3))
end
set(gca,'xTick',0:pi/2:4*pi) 
set(gca,'xTickLabel',{'0', ' ', 'pi', ' ', '2pi', ' ', '3pi', ' ', '4pi'})
% Define y-ticks and let them be auto-labelled... 
set(gca,'yTick',-5:.5:1)

title('1/ (cos(x) – c)') xlabel('x') ylabel('y') legend('y(0)= 1','y(pi/2)= -1/2', 'y(pi/2)= 1/2', 'y(pi/2)= -2/3', 'y(pi/2)= 2/3', 'y(pi/2)= -1', 'y(pi/2)= 1')

end
<</matlabcentral/answers/uploaded_files/27185/assignment3_2b.jpg>>

Any help would be appreciated.

Best Answer

How good are you!

Thanks

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MATLAB: Error using surf X, Y, Z, and C cannot be complex error

this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>

The problem is not in solving

x = 0:0.8:pi;
A = sin(x).^(1/3)
B = cos(x).^(1/3)

the operator

.^

solves for either real or complex.

The problem lays in the fact that surf doesn't take in complex values.

To solve the long expression of H, since you are dealing with complex numbers, you have to plot 2 surfs, not one: Real and Imaginary, or Modulus and Phase

clc
theta5=[0:0.1:pi];
theta4=[0:0.1:pi];
[X,Y]=meshgrid(theta4,theta5);
H=(((((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2*sin(X).^2+cos(Y).^2.*sin(X).^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(Y).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27+(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2-cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^2-((cos(X).^2.*cos(Y).^2)./3-(cos(X).^2.*sin(X).^2)./3+(cos(Y).^2.*sin(X).^2)./3+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(X).^2+sin(X).^2.*sin(Y).^2).^2./9+(cos(X).^2*cos(Y).^4.*sin(X).^2)./3+(2.*cos(X).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(Y).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(X).^2.*sin(X).^2.*sin(Y).^4)./3).^3).^(1/2)-((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2.*sin(X).^2+cos(Y).^2.*sin(X).^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2.*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(Y).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6-(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27-(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2+cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^(1/3)+cos(X).^2./3-cos(Y).^2./3+sin(X).^2./3+((cos(X).^2.*cos(Y).^2)./3-(cos(X).^2.*sin(X).^2)./3+(cos(Y).^2.*sin(X).^2)./3+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^2./9+(cos(X).^2.*cos(Y).^4.*sin(X).^2)./3+(2*cos(X).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(Y).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(X).^2.*sin(X).^2.*sin(Y).^4)./3)./(((((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2.*sin(X).^2+cos(Y).^2.*sin(X).^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2.*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(X).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27+(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2-(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2-cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^2-((cos(X).^2.*cos(Y).^2)./3-(cos(X).^2.*sin(X).^2)./3+(cos(Y).^2.*sin(X).^2)./3+(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^2./9+(cos(X).^2.*cos(Y).^4.*sin(X).^2)./3+(2.*cos(X).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(Y).^2.*sin(X).^2.*sin(Y).^2)./3-(cos(X).^2.*sin(X).^2.*sin(Y).^4)./3).^3).^(1/2)-((cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).*(cos(X).^2.*cos(Y).^2-cos(X).^2.*sin(X).^2+cos(Y).^2.*sin(X)^2+cos(X).^2.*cos(Y).^4.*sin(X).^2+2.*cos(X).^2.*sin(X).^2.*sin(Y).^2-cos(Y).^2.*sin(X).^2.*sin(Y).^2-cos(X).^2.*sin(X).^2.*sin(Y).^4))./6-(cos(Y).^2-cos(X).^2-sin(X).^2+cos(X).^2.*sin(Y).^2+sin(X).^2.*sin(Y).^2).^3./27-(cos(X).^2.*cos(Y).^2.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^6.*sin(X).^2)./2+(cos(X).^2.*cos(Y).^2.*sin(X).^2.*sin(Y).^2)./2+cos(X).^2.*cos(Y).^4.*sin(X).^2.*sin(Y).^2).^(1/3)-(cos(X).^2.*sin(Y).^2)./3-(sin(X).^2.*sin(Y).^2)./3;
figure(1);surf(X,Y,abs(H))
figure(2);surf(X,Y,angle(H))

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance for time and attention

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

MATLAB: How to add a less than constraint condition to solve the transcendental equation

    A=[1,-1,0,0;
       0, 1,-1;0;
       0, 0, 1,-1];
    b=[0;0;0];
   objFcn =@myFitnes;
  nvars = 4;
  LB = [0 0 0 0];
  UB = [pi/2 pi/2 pi/2 pi/2];
  [x, fval] = ga(objFcn,nvars,A,b,[],[],LB,UB);

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MATLAB: Error using surf X, Y, Z, and C cannot be complex error

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