How to use of trigonometric identities in matlab?

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?

Answer 1

[Star Strider]

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]

[Naseeb Gill]

Thanks @Star S. It works perfectly.

[Star Strider]

My pleasure.

[Naseeb Gill]

Hello Star S. I have one little query here. If I want to substitute the values of l1 th1 r11 r12 r13 r21 r22 r23 r31 r32 r33 px py pz all these variables in my final matrix. How I should do?

[Star Strider]

The easiest way is to use the matlabFunction function to create an anonymous function from ‘inv2’:

inv2_fcn = matlabFunction(inv2);

creating (after a little editing so it is on one line and a bit easier to read):

inv2_fcn = @(l1,px,py,pz,r11,r12,r13,r21,r22,r23,r31,r32,r33,th1) reshape([r11.*cos(th1)+r21.*sin(th1),r21.*cos(th1)-r11.*sin(th1),r31,0.0,r12.*cos(th1)+r22.*sin(th1),r22.*cos(th1)-r12.*sin(th1),r32,0.0,r13.*cos(th1)+r23.*sin(th1),r23.*cos(th1)-r13.*sin(th1),r33,0.0,px.*cos(th1)+py.*sin(th1),py.*cos(th1)-px.*sin(th1),-l1+pz,1.0],[4,4]);

then use it as you would any other function.

Answer 2

[Abdulsalam]

how to write this equation?