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MathGroup Archive 2004

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Re: How to solve a simple Trig cofunction?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50547] Re: [mg50500] How to solve a simple Trig cofunction?
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 9 Sep 2004 05:19:25 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

soln = Reduce[
    {Cos[x+4]==Sin[3x+2], 
      0<=x<=Pi/2},x]

x == (1/2)*(-3 + 2*Pi - 2*ArcTan[1 + Sqrt[2]])

To convert to degrees:

soln /. a_?NumericQ :> a/Degree // 
  FunctionExpand

x == (90*(-3 + 2*Pi - 2*ArcTan[1 + Sqrt[2]]))/Pi

%//N

x == 26.556330730376516

Select[NSolve[Cos[x+4]==Sin[3x+2], x], 
    0<=(x/.#)<=Pi/2&] /. 
  a_?NumericQ :> a/Degree

{{x -> 26.55633073037652}}


Bob Hanlon

> 
> From: bfeeny at mac.com (Brian Feeny)
To: mathgroup at smc.vnet.net
> Date: 2004/09/08 Wed AM 05:14:59 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg50547] [mg50500] How to solve a simple Trig cofunction?
> 
> Lets say I have:
> 
> cos[X+4] = sin[3X+2]
> 
> What would be the proper way to solve the above, for X, in
> Mathematica, with the answer in degrees?
> 
> I did this, but something tells me their has to be a better way:
> 
> NSolve[Cos[X Degree +4 Degree] = Sin[3 X Degree+2 Degree], X]
> 
> I mean, I wish i didn't have to enter "Degree"so many times, perhaps
> their is a simple way to just tell it the whole thing is in Degree.
> 
> Additionally, is their a way to constrain the above to 90 > X > 0?  I
> tried doing like:
> 
> NSolve[Cos[X Degree +4 Degree] = Sin[3 X Degree+2 Degree], X /; 90
> >X>0]
> 
> but that obviously is not the right way since that doesn't work. 
> Appreciate all the help.
> 
> Brian
> 
> 


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