Solving Multiple Transcendental Equations

I asked this earlier but the way I asked it was completely wrong so let me try this again.

The two equations I have are:

    200.*sin(b)==190.+80.*cos(x)-240.*cos(g);
    200.*cos(b)==70.+80.*sin(x)+240.*sin(g);

And I want b = f(x) and g = f(x).

Whenever I use solve() I get an array of a solution because of acos() and after that I get lost.

Any help would be great. thanks.

Answer 1

[Walter Roberson]

There are no arcsine or arccosine in the solutions

1)

b = arctan((534755-195776*cos(2*x)+86464*sin(2*x)-52480*cos(3*x)+404296*cos(x)+410704*sin(x)+(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2))/(1847400-524800*cos(2*x)+1061760*sin(x)), ((8*cos(x)+19)*(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2)-869440*cos(x)+214016*cos(3*x)+1080576*sin(3*x)-5668320*sin(x)+3083744*cos(2*x)-209920*cos(4*x)-3472065-749056*sin(2*x))/(-17178840-24310720*sin(x)+7920640*cos(2*x)+2099200*sin(3*x)))

g = arctan(((8*cos(x)+19)*(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2)+7402673+11296096*sin(x)-869440*cos(x)-4970464*cos(2*x)-1238272*sin(3*x)-749056*sin(2*x)+214016*cos(3*x)+209920*cos(4*x))/(-20614608-29172864*sin(x)+9504768*cos(2*x)+2519040*sin(3*x)), (1220275-302784*cos(2*x)+125888*sin(2*x)-52480*cos(3*x)+229704*cos(x)+597968*sin(x)-(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2))/(2216880-629760*cos(2*x)+1274112*sin(x)))

2)

b = arctan((534755-195776*cos(2*x)+86464*sin(2*x)-52480*cos(3*x)+404296*cos(x)+410704*sin(x)-(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2))/(1847400-524800*cos(2*x)+1061760*sin(x)), ((-8*cos(x)-19)*(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2)-869440*cos(x)+214016*cos(3*x)+1080576*sin(3*x)-5668320*sin(x)+3083744*cos(2*x)-209920*cos(4*x)-3472065-749056*sin(2*x))/(-17178840-24310720*sin(x)+7920640*cos(2*x)+2099200*sin(3*x)))

g = arctan(((-8*cos(x)-19)*(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2)+7402673+11296096*sin(x)-869440*cos(x)-4970464*cos(2*x)-1238272*sin(3*x)-749056*sin(2*x)+214016*cos(3*x)+209920*cos(4*x))/(-20614608-29172864*sin(x)+9504768*cos(2*x)+2519040*sin(3*x)), (1220275-302784*cos(2*x)+125888*sin(2*x)-52480*cos(3*x)+229704*cos(x)+597968*sin(x)+(1640791313840*sin(x)-467972670336*cos(x)-219593805312*sin(3*x)-506590930944*sin(2*x)[phone]*cos(3*x)-785914163168*cos(2*x)-15571025920*cos(5*x)[phone]*sin(4*x)-4655185920*sin(5*x)[phone]*cos(6*x)[phone]*cos(4*x)[phone])^(1/2))/(2216880-629760*cos(2*x)+1274112*sin(x)))

Obvious once you see it, right? ;-)

[Keith Szkodny]

Is there any way to numerically solve this instead of symbolically?

[Walter Roberson]

You want a numeric solution that gives b and g as a function of x ??