how to make make matlab compute values of simple trignometric identities?

cos(pi/2 + theta)= - sin(theta) ;

sin(pi + theta) = - sin(theta) ;

how do i compute these in MATLAB !

Here's my code ... (without identities its difficult to solve further)

syms L1 th1 L2 th2 L3 th3 th4 L5 th5;
a=[0 L2 L3 0 0];
alp=sym([(pi/2) 0 0 pi/2 0]);
d= [L1 0 0 0 L5];
th=sym([th1 th2+pi/2 th3-pi/2 th4+pi/2 th5]);
T=eye(4);
n= 5 ;
for i=1:n
    switch i;
        case 1
            T01 =[cos(th(i)) -sin(th(i))*cos(alp(i)) sin(th(i))*sin(alp(i)) a(i)*cos(th(i));
                sin(th(i)) cos(th(i))*cos(alp(i)) -sin(alp(i))*cos(th(i)) a(i)*sin(th(i)); 
                0 sin(alp(i)) cos(alp(i)) d(i) ;
                0 0 0 1]
        case 2
            T12 =[cos(th(i)) -sin(th(i))*cos(alp(i)) sin(th(i))*sin(alp(i)) a(i)*cos(th(i));
                sin(th(i)) cos(th(i))*cos(alp(i)) -sin(alp(i))*cos(th(i)) a(i)*sin(th(i)); 
                0 sin(alp(i)) cos(alp(i)) d(i) ;
                0 0 0 1]    
    trignometr    case 3
            T23 =[cos(th(i)) -sin(th(i))*cos(alp(i)) sin(th(i))*sin(alp(i)) a(i)*cos(th(i));
                sin(th(i)) cos(th(i))*cos(alp(i)) -sin(alp(i))*cos(th(i)) a(i)*sin(th(i)); 
                0 sin(alp(i)) cos(alp(i)) d(i) ;
                0 0 0 1]
        case 4
            T34 =[cos(th(i)) -sin(th(i))*cos(alp(i)) sin(th(i))*sin(alp(i)) a(i)*cos(th(i));
                sin(th(i)) cos(th(i))*cos(alp(i)) -sin(alp(i))*cos(th(i)) a(i)*sin(th(i)); 
                0 sin(alp(i)) cos(alp(i)) d(i) ;
                0 0 0 1]    
        case 5
            T45 =[cos(th(i)) -sin(th(i))*cos(alp(i)) sin(th(i))*sin(alp(i)) a(i)*cos(th(i));
                sin(th(i)) cos(th(i))*cos(alp(i)) -sin(alp(i))*cos(th(i)) a(i)*sin(th(i)); 
                0 sin(alp(i)) cos(alp(i)) d(i) ;
                0 0 0 1]
    end
end
T05=T01*T12*T23*T34*T45

Answer 1

[the cyclist]

Do you mean you want to solve for theta, in the equation

cos(pi/2 + theta)= - sin(theta);

?

Use solve.

[Mayank Ghugretkar]

yes

it computes for (pi + theta) but cant get it to compute cos(pi/2 + theta)= - sin(theta);

[the cyclist]

I'm unclear on what you mean by "can't get it to compute". Does it throw an error? It should just give theta=0 right?

(I don't have the symbolic math toolbox, so I can't try this myself.)

Answer 2

[Star Strider]

If necessary, use the simplify function.

Example:

syms theta 
Eq = sin(pi + theta)
Out = simplify(Eq, 'Steps',250)

This also works for your ‘T’ equations, although there is significant simplification by default, without a specific simplify call needed.