3 eq 3 unknowns big mess

Hi, Pls help me solve these 3 equation with 3 unknowns and explain how its done:

1) (7939*cos(y)*sin(z))/100 - (9*cos(y)*cos(z))/20 - (367*sin(y))/50 + 441/200 = 0

2) (7939*cos(x)*cos(z))/100 + (367*cos(y)*sin(x))/50 + (9*cos(x)*sin(z))/20 - (9*cos(z)*sin(x)*sin(y))/20 + (7939*sin(x)*sin(y)*sin(z))/100 + 7263/100 = -75

3) (367*cos(x)*cos(y))/50 - (7939*cos(z)*sin(x))/100 - (9*sin(x)*sin(z))/20 - (9*cos(x)*cos(z)*sin(y))/20 + (7939*cos(x)*sin(y)*sin(z))/100 - 387/100 = 0

At least give me an answer even if it takes mathematica because even that is not giving out answers.

Answer 1

[Oleg Komarov]

With the optimization tb:

f=@(x)[7939*cos(x(2))*sin(x(3))/100-9*cos(x(2))*cos(x(3))/20-367*sin(x(2))/50+441/200;
       7939*cos(x(1))*cos(x(3))/100+367*cos(x(2))*sin(x(1))/50+9*cos(x(1))*sin(x(3))/20-9*cos(x(3))*sin(x(1))*sin(x(2))/20+7939*sin(x(1))*sin(x(2))*sin(x(3))/100+7263/100+75;
       367*cos(x(1))*cos(x(2))/50-7939*cos(x(3))*sin(x(1))/100-9*sin(x(1))*sin(x(3))/20-9*cos(x(1))*cos(x(3))*sin(x(2))/20+7939*cos(x(1))*sin(x(2))*sin(x(3))/100-387/100];

EDIT

f = @(x) [2.79 * cos(x(2))*sin(x(2)) - 76.1*sin(x(1))*sin(x(2)) - 2.06*cos(x(2))*cos(x(2)) + 2.06*cos(x(1))*sin(x(2))*sin(x(2)) + 2.79*cos(x(1))*cos(x(2))*sin(x(2));
          75 - 2.79*cos(x(2))*sin(x(1)) - 2.06*sin(x(1))*sin(x(2)) - 76.1*cos(x(1));
          76.1*cos(x(2))*sin(x(1)) - 2.06*cos(x(2))*sin(x(2)) + 2.79*sin(x(2))*sin(x(2)) - 2.79*cos(x(1))*cos(x(2))*cos(x(2)) - 2.06*cos(x(1))*cos(x(2))*sin(x(2))]
opt = optimset('MaxFunEvals',500);
R   = fsolve(f,[0 0 0],opt)

[Zoheb Akhtar]

Hey Oleg,

Thanks a lot for the effort, would you please help me with these equations instead, I found out few mistakes in the previous one. By the way why are you using the parameters (2), (3) etc in the x(), y() and z()'s?

Thanks

Solve[2.79*Cos[y]*Sin[y] - 76.1*Sin[x]*Sin[y] - 2.06*Cos[y]*Cos[y] +

2.06*Cos[x]*Sin[y]*Sin[y] + 2.79*Cos[x]*Cos[y]*Sin[y] == 0,

75 - 2.79*Cos[y]*Sin[x] - 2.06*Sin[x]*Sin[y] - 76.1*Cos[x] == 0,

76.1*Cos[y]*Sin[x] - 2.06*Cos[y]*Sin[y] + 2.79*Sin[y]*Sin[y] -

2.79*Cos[x]*Cos[y]*Cos[y] - 2.06*Cos[x]*Cos[y]*Sin[y] ==

0, {x, y, z} Reals]

[Oleg Komarov]

It's a syntax constraint.

See the edit above.

Answer 2

[Walter Roberson]

My computation is that there are no simultaneous real roots for these equations. There might be imaginary roots.

If you consider the second and third equations together, two equations in three unknowns, and solve each of them for y, you get two pairs of solutions (in terms of x and z). As those two need to be equal, you can construct the list [sol2_A - sol3_A, sol2_B - sol3_A, sol2_A - sol3_B, sol2_B - sol3_B]. At least one member of the list must equal 0 somewhere over (x,z) in order for there to be a solution for the pair of equations. If you ask for a 3D plot of that values of that list over x = 0 to 2*Pi and z = 0 to 2*Pi, you will not get any plot because all members of the list evaluate to imaginary values over that entire range, at least to within the resolution of the plot.

(I also approached the problem in other ways, and with different pairs of variables, and each time found that either there were no solutions or that at least one value had to be imaginary.)

[Zoheb Akhtar]

Hi,

Thanks a lot for the effort you put in. I re calculated the whole equation and found few errors in it. May be that's the reason things didn't work out. I tried it yet again in Mathematica but got no answer. I would really appreciate if you could try it once with these revised equations below:

Solve[2.79*Cos[y]*Sin[y] - 76.1*Sin[x]*Sin[y] - 2.06*Cos[y]*Cos[y] +

2.06*Cos[x]*Sin[y]*Sin[y] + 2.79*Cos[x]*Cos[y]*Sin[y] == 0,

75 - 2.79*Cos[y]*Sin[x] - 2.06*Sin[x]*Sin[y] - 76.1*Cos[x] == 0,

76.1*Cos[y]*Sin[x] - 2.06*Cos[y]*Sin[y] + 2.79*Sin[y]*Sin[y] -

2.79*Cos[x]*Cos[y]*Cos[y] - 2.06*Cos[x]*Cos[y]*Sin[y] ==

0, {x, y, z} Reals]

Thanks a ton

[Walter Roberson]

Not possible. You ask to solve for z, but you do not have any z in your expressions.