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Re: how to minimize a trigonometric function with some

• To: mathgroup at smc.vnet.net
• Subject: [mg96368] Re: [mg96323] how to minimize a trigonometric function with some
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 12 Feb 2009 06:38:30 -0500 (EST)
• References: <200902111024.FAA17258@smc.vnet.net>
• Reply-to: drmajorbob at longhorns.com

Repost with proper syntax (copy as plain text from Mathematica). I can  
only guess you meant

f[t_] = a*Sin[t] - x0^2 + (b*Cos[t] - y0)^2

but I got that by deleting the unmatched parenthesis. If you accidentally  
left one out, I have the wrong function.

Maybe you meant

f[t_] = (a*Sin[t] - x0)^2 + (b*Cos[t] - y0)^2

Either way, you can proceed (for given values of the parameters) with

g[a_?NumericQ, b_?NumericQ, x0_?NumericQ, y0_?NumericQ] =
  Minimize[f@t, t];

g[1, 2, 3, 4]

{25 - 16 Cos[2 ArcTan[Root[-3 + 10 #1 + 22 #1^3 + 3 #1^4 &, 2]]] +
   4 Cos[2 ArcTan[Root[-3 + 10 #1 + 22 #1^3 + 3 #1^4 &, 2]]]^2 -
   6 Sin[2 ArcTan[Root[-3 + 10 #1 + 22 #1^3 + 3 #1^4 &, 2]]] +
   Sin[2 ArcTan[Root[-3 + 10 #1 + 22 #1^3 + 3 #1^4 &, 2]]]^2, {t ->
    2 ArcTan[Root[-3 + 10 #1 + 22 #1^3 + 3 #1^4 &, 2]]}}

N@%

{11.3921, {t -> 0.508687}}

Bobby

On Wed, 11 Feb 2009 04:24:04 -0600, tomt <tomtforever at gmail.com> wrote:

> f(t)=a*Sin[t] - x0)^2 + (b*Cos[t] - y0)^2.
> t is variable,others is const.
> 0<=t<2*Pi,a>0,b>0
>
> I have tried it again and again in mathematica ,but can't get a right  
> result
>



-- 
DrMajorBob at longhorns.com

• References:
  • how to minimize a trigonometric function with some symbol const
    • From: tomt <tomtforever@gmail.com>