Error while plotting the polar plot

%I have an expression which is plotted using the polarplot.

a = 1/(2.*cos(theta))

e = 0.5;
thet = -60:1:60;
theta = thet .*(pi/180);
c = cos(theta);
p = 4*(1-e^2).*(c.^2) + (2*e - 1)^2;
q = 2*(1-e*e).*c + (2e-1)*sqrt(4*(1-e*e).*(c.^2) + 5 *e*e - 4*e);
r = q./p;
polarplot(theta,r);
hold on;

%Now if i solve the expresion for e=0.5 analytically and then try plotting the expression

a = 1./(2.*cos(theta));
polarplot(theta,a);
hold off;

%Why the graphs are not same while both the expressions are same.

Answer 1

[Chunru]

e = 0.5;
thet = -60:1:60;
theta = thet .*(pi/180);
c = cos(theta);
p = 4*(1-e^2).*(c.^2) + (2*e - 1)^2;

% q = 2*(1-e*e).*c + (2e-1)*sqrt(4*(1-e*e).*(c.^2) + 5 *e*e - 4*e);

% 2e-1 is the number 2x10^(-1), rather than 2*e-1 !!!

q = 2*(1-e*e).*c + (2*e-1)*sqrt(4*(1-e*e).*(c.^2) + 5 *e*e - 4*e);
r = q./p;

polarplot(theta,r);
hold on;

a = 1./(2.*cos(theta));
polarplot(theta,a);
hold off;

[CHANDRABHAN Singh]

Thanks.