MATLAB: Symbolic substitution in matrices

symbolic substitution

I was writing this symbolic matrix in matlab, and I wanted to substitute values for "x" in sin(x) and cos(x), but it didn't give me the actual value of the sin(x), only an expression like: sin(30) in the matrix, and also it didn't compute divisions and all other computations. I couldn't find the problem with the code. Please guide me to find the right way to write this code. example of the expression in the answer, after substitution: (3^(1/2)*(cos(pi/9)*sin(pi/18))
This is the code:
syms t1 t2 t3 L1 L2 L3
a=0; al=0; d=0; ct1=cos(t1); st1=sin(t1); sal=sin(al); cal=cos(al); T01=[ct1 -st1 0 a;st1*cal ct1*cal -sal -d*sal;st1*sal ct1*sal cal d*cal;0 0 0 1];
a=L1; al=0; d=0; ct2=cos(t2); st2=sin(t2); sal=sin(al); cal=cos(al); T12=[ct2 -st2 0 a;st2*cal ct2*cal -sal -d*sal;st2*sal ct2*sal cal d*cal;0 0 0 1];
a=L2; al=0; d=0; ct3=cos(t3); st3=sin(t3); sal=sin(al); cal=cos(al); T23=[ct3 -st3 0 a;st3*cal ct3*cal -sal -d*sal;st3*sal ct3*sal cal d*cal;0 0 0 1];
a=L3; T3H=[1 0 0 a;0 1 0 0;0 0 1 0;0 0 0 1];
T03=T01*T12*T23; T0H=T03*T3H;
disp('T03 for t1=0 t2=0 t3=0 :') subs(T03,[t1,t2,t3],[0,0,0])
disp('T0H for t1=0 t2=0 t3=0 :') subs(T0H,[t1,t2,t3],[0,0,0])
t11=pi*(10/180); t21=pi*(20/180); t31=pi*(30/180); disp('T03 for t1=10 t2=20 t3=30 :') T03n=subs(T03,[t1,t2,t3],[t11,t21,t31])
disp('T0H for t1=10 t2=20 t3=30 :') T0Hn=subs(T0H,[t1,t2,t3],[t11,t21,t31])
t12=pi*(1/2); t22=pi*(1/2); t32=pi*(1/2); disp('T03 for t1=90 t2=90 t3=90 :') T03n=subs(T03,[t1,t2,t3],[t12,t22,t32])
disp('T0H for t1=90 t2=90 t3=90 :') T0Hn=subs(T0H,[t1,t2,t3],[t12,t22,t32])

Best Answer

vpa(T03n)
vpa(T0Hn)
help vpa
VPA Variable precision arithmetic.
R = VPA(S) numerically evaluates each element of the double matrix S using variable precision floating point arithmetic with D decimal digit accuracy, where D is the current setting of DIGITS.
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