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Re: General--Another Trigonometric Problem....NEED HELP
*To*: mathgroup at smc.vnet.net
*Subject*: [mg71065] Re: General--Another Trigonometric Problem....NEED HELP
*From*: "dimitris" <dimmechan at yahoo.com>
*Date*: Wed, 8 Nov 2006 06:02:25 -0500 (EST)
*References*: <eijobs$l9v$1@smc.vnet.net>
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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