How to solve for a in r = xsin(a) + ysin(a+b) + zsin(a+b+c); x,y,z,b,c are constant?

[tryptophan13]

Hi, first time post so I apologise if it is poorly formed or in the wrong place.

I'm trying to position a robot arm using knowledge of how far away the end should be, but that's not important for this question.

My question is: how can you solve for a single angle variable when it appears in several sin or cos terms with different coefficients?

The problem, specifically, is for a known value R in the equation R = C1*sin(A) + C2*sin(A+const1) + C3*sin(A+const1+const2), how can one rearrange to make A the subject? I feel sure this must be possible since there is only a single unknown (A) and all other elements are constant, but it's been many years since I even looked at a trig identity and I'm kind of at a loss for even where to begin

Any suggestions would be greatly appreciated
Thank you

 

[sinx]

Hi, first time post so I apologise if it is poorly formed or in the wrong place.

I'm trying to position a robot arm using knowledge of how far away the end should be, but that's not important for this question.

My question is: how can you solve for a single angle variable when it appears in several sin or cos terms with different coefficients?

The problem, specifically, is for a known value R in the equation R = C1*sin(A) + C2*sin(A+const1) + C3*sin(A+const1+const2), how can one rearrange to make A the subject? I feel sure this must be possible since there is only a single unknown (A) and all other elements are constant, but it's been many years since I even looked at a trig identity and I'm kind of at a loss for even where to begin
Any suggestions would be greatly appreciated

Thank you

sin(a+b)=sinacosb+cosasinb