MATLAB: How to use of trigonometric identities in matlab

matricestrigonometric

I want to do some matrix multiplication which include symbolic variables and sine and cosine function. Code is given below.
    syms ('l1','th1''r11', 'r12', 'r13','r21', 'r22','r23','r31','r32','r33', 'px','py', 'pz');
    A0_1 = [cos(th1) -sin(th1) 0 0 ; sin(th1) cos(th1) 0 0; 0 0 1 l1; 0 0 0 1];
     EE = [r11 r12 r13 px; r21 r22 r23 py; r31 r32 r33 pz; 0 0 0 1] ;
     inv1 = inv(A0_1)*EE;
Multiplied matrix include trigonometric identities like (cos(th1)^2 + sin(th1)^2) so I want to convert these trigonometric identities into its values like 1 in above case. How to do this?

Best Answer

Use the simplify function:
syms l1 th1 r11 r12 r13 r21 r22 r23 r31 r32 r33 px py pz
A0_1 = [cos(th1) -sin(th1) 0 0 ; sin(th1) cos(th1) 0 0; 0 0 1 l1; 0 0 0 1];
EE = [r11 r12 r13 px; r21 r22 r23 py; r31 r32 r33 pz; 0 0 0 1] ;
inv1 = A0_1\EE;
inv2 = simplify(inv1)
inv2 =
[ r11*cos(th1) + r21*sin(th1), r12*cos(th1) + r22*sin(th1), r13*cos(th1) + r23*sin(th1), px*cos(th1) + py*sin(th1)]
[ r21*cos(th1) - r11*sin(th1), r22*cos(th1) - r12*sin(th1), r23*cos(th1) - r13*sin(th1), py*cos(th1) - px*sin(th1)]
[                         r31,                         r32,                         r33,                   pz - l1]
[                           0,                           0,                           0,                         1]
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