Solving for 2 Unknowns with 3 Equations and Sine Functions

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Discussion Overview

The discussion revolves around solving a system of three equations with two unknowns, incorporating sine functions and constants. Participants seek assistance in finding solutions to the equations, which involve trigonometric identities and algebraic manipulation.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents an initial system of equations involving sine functions and constants, asking for help in finding a solution.
  • Another participant questions the accuracy of the second equation in the initial system, suggesting a possible correction.
  • A subsequent post proposes a revised system of equations, indicating that the original equations were incorrect and requesting further assistance.
  • One participant suggests using trigonometric identities to simplify the equations and proposes a method to eliminate one variable through algebraic manipulation.
  • Another participant notes that with three equations and two constants, it should be possible to combine the equations to reduce the number of unknowns.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correctness of the initial equations, with some proposing corrections. There is no consensus on the best method to solve the equations, and multiple approaches are suggested.

Contextual Notes

Participants have not fully resolved the assumptions underlying the equations, and there are indications of potential errors in the formulation of the equations. The discussion remains exploratory, with various methods proposed for approaching the problem.

boeledi
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Could someone help me find the solution of this ?

x - y + z - 2 A sin(y+z) = C
-x - y - z - 2 A sin(x+z) = C
-x + y + z - 2 A sin(x+y) = C

Where C and A are constant ?
Many thanks
 
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could you please confirm that the second line is not x + y - z ...
 
Sorry, based on your question, I did my calculations again and ... The real system is:

-x + y + z + 2A sin(y-z) = C
-x + y - z + 2A sin(x-z) = C
x + y - z + 2A sin(x-y) = C

where A and C are constant.

Could you please help me?
 
I would start by applying the trigonometric identities for sin(a+b) then add the first 2 equations together. I think several terms will drop out, you then should be able to repeat the process with the 3rd equation. The goal is to eliminate one of the variables, when you have an expression involving 2 variables solve for 1 of them, then use that to back substitute isolating the remaining variables.
 
5 unkowns
2 of which are constant
3 equations

combine 3 equations, you will be left with 2 unkowns (your two constants)

And you are done... all you need is the time to solve it.
 

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