How to plot Leminscate shape using Matlab?

Question

How to plot this Leminscate (−π/4 =< φ =< π/4) ?

x = cos(φ)sqrt(2cos(2φ))
y = sin(φ)sqrt(2cos(2φ))

This is my attempt:

x = -pi/4:0.001:pi/4;
xy = cos(x).*sqrt(2*cos(2.*x));
yy = sin(x).*sqrt(2*cos(2.*x));
plot(x,xy,x,yy)
axis equal
grid on

Result

Answer 1

Following code segment may help you to find the solution. Next time, please clearly mention what you have tried and any error messages you saw.

x = -pi/4:pi/256:pi/4;

yx = cos(x).*sqrt(2*cos(2.*x));
yy = sin(x).*sqrt(2*cos(2.*x));

plot(x,yx,x,yy);

Answer 2

theta = linspace (-pi/4,pi/4);
x = cos(theta).*sqrt(2.*cos(2.*theta));
y = sin(theta).*sqrt(2.*cos(2.*theta));
plot(x,y,-x,-y), grid on, 
axis ('equal')

result