MATLAB: Strange result from symbolic processing

Question

Hello,

I created this variables, some symbolic, some not:

alpha = [pi/2 0 0];
a = sym('[0 a2 a3]');
d = [0 0 0];
theta = sym('t', [1,3]);

initializing….

C = (zeros(1, 2, 2));

and I create the element (:,:,1) as:

 C(:,:,1) = [(cos(theta(1))) (-sin(theta(1)))*cos(alpha(1))];

but it returns me this error:

The following error occurred converting from sym to
double:
Error using mupadmex
Error in MuPAD command: DOUBLE cannot convert the input
expression into a double array.
If the input expression contains a symbolic variable, use
the VPA function instead.

so I tried to set:

C = vpa(zeros(1, 2, 2));

and so it returns a strange result

C(:,:,1) = 
[ cos(t1), -(4967757600021511*sin(t1))/81129638414606681695789005144064]

but if cos(pi/2)=0 it should be

(-sin(theta(1)))*cos(alpha(1)) = 0

what is that long (and wrong) number ?

Answer 1

alpha = [pi/2 0 0];

does not define alpha(1) as the theoretical Pi/2. Instead, it defines alpha(1) as the double precision approximation to pi/2, which is not exactly Pi/2 and so cos() of it is not exactly 0.

Better use

alpha = sym('[pi/2 0 0]');