Calculate a letter from equation with letters.

Hello.

I am just wondering that how I can calculate a letter from the equation with letters. For example here,

if I want to get cos1 and sin1 from these equation, how do I need to type the function??

syms Xe Ye a1 a2 cos1 cos2 sin1 sin2
Xe = a2*(cos1*cos2-sin1*sin2)+a1*cos1;
Ye = a2*(sin1*cos2)+a1*sin1;

Thank you in advance.

Answer 1

[KSSV]

syms Xe Ye a1 a2 cos1 cos2 sin1 sin2
eqn1=Xe == a2*(cos1*cos2-sin1*sin2)+a1*cos1;
eqn2=Ye == a2*(sin1*cos2)+a1*sin1;
sol = solve([eqn1, eqn2],cos1,sin1) 
sol.sin1
sol.cos2

[Joji Mori]

Thank you! That is what I want it!

Answer 2

[Walter Roberson]

syms Xe Ye a1 a2 cos1 cos2 sin1 sin2
Xe = a2*(cos1*cos2-sin1*sin2)+a1*cos1;
Ye = a2*(sin1*cos2)+a1*sin1;

sol = solve([Xe,Ye],[sin1,cos1])

sol =

struct with fields:

sin1: [1×1 sym]

cos1: [1×1 sym]

>> sol.sin1

ans =

0

>> sol.cos1

ans =

0

Answer 3

[Stephan]

You might want to do this:

syms Xe Ye a1 a2 cos1 cos2 sin1 sin2
eq(1) = Xe == a2*(cos1*cos2-sin1*sin2)+a1*cos1;
eq(2) = Ye == a2*(sin1*cos2)+a1*sin1;

sin1_sol = isolate(eq(2),sin1);
cos1_sol = isolate(eq(1),cos1);
cos1_sol = subs(cos1_sol,sin1,rhs(sin1_sol));
pretty(sin1_sol)
pretty(cos1_sol)

results in:

             Ye
sin1 == ------------
        a1 + a2 cos2

              Ye a2 sin2
        Xe + ------------
             a1 + a2 cos2
cos1 == -----------------
           a1 + a2 cos2