Solveing Triq system of eqn

[MichaelLisowski]

I want to solve the equations below for Va and Ha given Vb and Hb. I have seen mathcad solve for coefficents of linear systems of equations but can mathcad solve these leaving the trig functions?

Vb=atan(tand(Va)/cos(Ha)); Va and Ha in degrees

Hb= asin(cos(VA)*sin(Ha)); Va and Ha in degrees

[RichardJ]

If you mean solve them numerically, yes. Look up solve blocks in the help.

[wayne]

By the way,

These are nonlinear equations, so look for that in help also. I took a quick stab at solving for one angle and substituting into the other equation and using solve, and back substitute, and it can find a symbolic solutionS that way, and its ugly. Makes me want to question the equations first. I may have made a mistake, but I am pretty sure its really ugly.

[AlanStevens]

wayne wrote:

By the way,

.... I took a quick stab at solving for one angle and substituting into the other equation and using solve, and back substitute, and it can find a symbolic solutionS that way, and its ugly. Makes me want to question the equations first. I may have made a mistake, but I am pretty sure its really ugly.

Ugly it is! Mathcad needs a lot of help on this one. See attached.

Alan

[MichaelLisowski]

Thanks for the help.

I think I got the solve block code working see the attached file.

Vb Hb Va Ha

5.02 4.98 5 5

7.05 44.78 5 45

27.24 41.64 20 45

I agree that the equations got ugly. They came out of a spec and I tryied to hand solve them but git lost in the process. I reviewed the file you sent me and the second equation should have been sin(Hb)=cos(Va)Sin(Ha) (multiplication)

I will see If I can use your format and modify it.

Thanks for your help

[RichardJ]

The equations are now less ugly, but I still wouldn't want to do it by hand.

[MichaelLisowski]

Thanks for the help. I still need to review the file in more detail before I even start to ask more questions.

[AlanStevens]

Note to self: read the question more carefully! Just for completeness, I attach my version with the (hopefully!) correct equations.

Alan

[RichardJ]

Note to self: read the question more carefully! Just for completeness,

Actually, I think the first post was edited. IIRC, the second equation originally had division, not multiplication.

[MichaelLisowski]

Thanks guys for all the help. I will review all the files.

As to the question on the first post to my knowledge it is unedited. I know I didn't change anything. I am sorry there was some sort of misunderstanding though. Once again thanks for all the help it definity saved me a whole bunch of paper and time.

[RichardJ]

I guess I need to read the question more carefully too then. The first time I typed everything into Mathcad I know I also had division in both equations, because I got the same answer Alan did

[LouP]

I took a similar approach, substituting names for cos(ha) and cos(va) and putting all of the ha-va dependence in terms of these, then solving. However, after seeing the results others got, I just solved on paper and came up woth a reasonably simple result (attached). I didn't bother typing the whole thing (not really that long on paper), but I did check the result. Both my solution and Alan's HaVa2 solutions(either the 0 or 1 subscript) check with the original equations, so they must be equivalent - but not so obvious by just looking.

Lou

[NormalVector]

Yes, solve blocks are amazing!

One thing to be wary about though: solve blocks solve the equations iteratively and thus depend on the initial guess you give. Just check your answers to see if they make sense.

[AlvaroDíaz]

Retyping some ideas.

Alvaro.