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Solve Four Trigonometric Equations Simultaneously?

Joseph Ninio
Posted 7 years ago

I am very new to the Wolfram Language and am trying to solve the below four equations simultaneously in Mathematica, but I receive the following error message:

"Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help."

I tried rounding these long numbers and converting them to fraction form, but I receive another error message:

"This system cannot be solved with the methods available to Solve."

Thanks in advance for any help.

Solve[{a*cos[b(88+c)]+d=5.981937616(88)-527.770953984,-a*b*sin[b(88+c)]=5.981937616,a*cos[b(120+c)]+d=-20,-a*b*sin[b(120+c)]=0},{a, b, c, d}]
POSTED BY: Joseph Ninio
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You should look up the basic syntax rules of the language. That said, I would solve first with respect to a,d, and then b,c:

solAD = Solve[
   Rationalize[{a*Cos[b (88 + c)] + d == 
      5.981937616 (88) - 527.770953984, 
     a*Cos[b (120 + c)] + d == -20}, 0],
   {a, d}] // Simplify; Solve[
 Rationalize[{-a*b*Sin[b (88 + c)] == 5.981937616,
    -a*b*Sin[b (120 + c)] == 0, Abs[b] < 10, Abs[c] < 10}, 0] /. 
  solAD[[1]],
 {b, c}, Reals]
POSTED BY: Gianluca Gorni
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