How to plot this implicit function？

x and y satisfy this implicit function:

10000^x*cos(x*pi/2)+10000^y*cos(y*pi/2)=0 (This implicit function cannot be transferred into the form as y=f(x) )

And z =(1000.^x).*sin(x*pi/2)*(10e-6)+(1000.^y).*sin(y*pi/2)*(10e-6);

Now how to plot (x,z)? I just use ezplot to plot (x,y), but I cannot pick up the concrete values of (x，y).

Answer 1

[Torsten]

Given x, calculate y from the relation

10000^x*cos(x*pi/2)+10000^y*cos(y*pi/2)=0

using MATLAB's fzero.

Then insert x and y in the relation

z =(1000.^x).*sin(x*pi/2)*(10e-6)+(1000.^y).*sin(y*pi/2)*(10e-6);

to calculate z.

Best wishes

Torsten.

[xiao dage]

Thank you for your answer!

The above graph is produced by

 ezplot('10000^x*cos(x*pi/2)+10000^y*cos(y*pi/2)=0',[0,4])

It can be seen that for one x, two or more values of y had been obtained is we expand the scope of x.

And with

 y=@(a)fzero(@(y) 10000^x*cos(x*pi/2)+10000^y*cos(y*pi/2),1);
 y1=y(0.1);

I can only calculate one y for one x, for example y1=y(0.1). So how to insert x and y in the relation

 z =(1000.^x).*sin(x*pi/2)*(10e-6)+(1000.^y).*sin(y*pi/2)*(10e-6);

to calculate z if I want to plot (x,z) in the scope of (0,2).

Answer 2

[Torsten]

xstart=0;
xend=2;
nx=10;
for i=1:nx+1
  x0=xstart+(i-1)/nx*(xend-xstart);
  x(i)=x0;
  y0=fzero(@(y) 10000^x0*cos(x0*pi/2)+10000^y*cos(y*pi/2),1);
  z(i)=(1000^x0)*sin(x0*pi/2)*(10e-6)+(1000^y0)*sin(y0*pi/2)*(10e-6);
end
plot(x,z)

Best wishes

Torsten.