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Re: General--Another Trigonometric Problem....NEED HELP


First things first.

All functions in Mathematica begin with Capital letter.
So it is Cos instead of cos and Sin instead of sin and so on...

Then = is the short notation for Set

Alias["="]
Set

E.g.

a = 3;

Information[a]
"Global`a"
a = 3

== (that is, two =) is needed for equations

Alias["=="]
Equal

Mathematica has a very clear syntax; it takes a while to learn the
basics (such as the above mentioned capitalization)
but as with all the systems you must first LEARN these basics before
starting use it!

Here is a good place to start; copy/paste in a notebook the following,
select the cell, and then execute the command

FrontEndExecute[{HelpBrowserLookup["MainBook", "1"]}]

For your problem now

Solve will give solutions but you are informed that some solutions may
be lost.

Solve[a*Sin[x] + b*Cos[x] == c, x]
Solve::ifun : Inverse functions are being used by Solve, so some
solutions
may not be found; use Reduce for complete solution information.
{{x -> -ArcCos[(c - (a^2*c)/(a^2 + b^2) - (a*Sqrt[a^2*b^2 + b^4 -
b^2*c^2])/(a^2 + b^2))/b]},
  {x -> ArcCos[(c - (a^2*c)/(a^2 + b^2) - (a*Sqrt[a^2*b^2 + b^4 -
b^2*c^2])/(a^2 + b^2))/b]},
  {x -> -ArcCos[(c - (a^2*c)/(a^2 + b^2) + (a*Sqrt[a^2*b^2 + b^4 -
b^2*c^2])/(a^2 + b^2))/b]},
  {x -> ArcCos[(c - (a^2*c)/(a^2 + b^2) + (a*Sqrt[a^2*b^2 + b^4 -
b^2*c^2])/(a^2 + b^2))/b]}}

(  FrontEndExecute[{HelpBrowserLookup["RefGuide", "Solve"]}]  )

For the complete set of equations use Reduce

Reduce[a*Sin[x] + b*Cos[x] == c, x]
(C[1] â?? Integers && ((a != 0 && a^2 + b^2 != 0 && c == -b && x ==
-2*ArcTan[b/a] + 2*Pi*C[1]) ||
    (c == -b && x == Pi + 2*Pi*C[1]))) || (b + c != 0 && C[1] â??
Integers &&
   ((-a^2 - b^2 - b*c + a*Sqrt[a^2 + b^2 - c^2] != 0 && x ==
2*ArcTan[(a - Sqrt[a^2 + b^2 - c^2])/(b + c)] + 2*Pi*C[1]) ||
    (a^2 + b^2 + b*c + a*Sqrt[a^2 + b^2 - c^2] != 0 && x == 2*ArcTan[(a
+ Sqrt[a^2 + b^2 - c^2])/(b + c)] + 2*Pi*C[1]))) ||
  ((-Pi + x)/(2*Pi) â?? Integers && a == 0 && b == 0 && c == 0)

(  FrontEndExecute[{HelpBrowserLookup["RefGuide", "Reduce"]}]  )

Regards
Dimitris


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