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Re: Solving a simple equation

• To: mathgroup at smc.vnet.net
• Subject: [mg121876] Re: Solving a simple equation
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Wed, 5 Oct 2011 04:04:14 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6e675$kds$1@smc.vnet.net>

"Daniel Kallfaß" <eizdealer at web.de> schrieb im Newsbeitrag 
news:j6e675$kds$1 at smc.vnet.net...
> Hi there, I wonder why the following equation cannot be solved:
>
> \[Kappa] = 1.4
> \[CapitalTheta] = 10;
> NSolve[Tan[\[Theta] degree] ==
>  2*Cot[\[Beta] degree]*(ma1^2*Sin[\[Beta] degree]^2 - 1)/(
>   ma1^2*(\[Kappa] + Cos[2 \[Beta] degree]) + 2), \[Beta]]
>
> It says: NSolve::nsmet: This system cannot be solved with the methods
> available to NSolve.
>
> Is there something I'm missing? My Voyage 200 solves it without any
> issues.
>
> Thanks,
> Daniel
>
The constant ma1 has no values assigned. If you set it (e.g. to 5) 
you'll get pretty normal solutions (see below).
PS: I changed angles to radians, hence Beta must be multiplied by 
180/Pi to get it in degrees.

Wolfgang

\[Kappa] = 1.4
\[Theta] = 10*(Pi/180);
ma1 = 5;
NSolve[Tan[\[Theta]] == 2*Cot[\[Beta]]*((ma1^2*Sin[\[Beta]]^2 - 
1)/(ma1^2*(\[Kappa] + Cos[2*\[Beta]]) + 2)), \[Beta]]

1.4

Solve::"ifun"\),
":", "\<\"Inverse functions are being used by (Solve), so some
solutions may not be found; use Reduce for complete solution 
information.


{{\[Beta] -> -2.8034174741802227}, {\[Beta] -> -1.615304107903905}, 
{\[Beta] -> -0.11913447310112904},
{\[Beta] -> 0.33817517940957037}, {\[Beta] -> 1.5262885456858881}, 
{\[Beta] -> 3.0224581804886643}}