Re: How to solve a simple Trig cofunction?

*To*: mathgroup at smc.vnet.net*Subject*: [mg50532] Re: [mg50500] How to solve a simple Trig cofunction?*From*: Brian Feeny <bfeeny at mac.com>*Date*: Thu, 9 Sep 2004 05:18:10 -0400 (EDT)*References*: <NDBBJGNHKLMPLILOIPPOGENGECAA.djmp@earthlink.net>*Sender*: owner-wri-mathgroup at wolfram.com

David, Thanks, I am learning alot from the multiple ways people here have helped me with this problem. I am confused however, why DrBob and Andrzej came up with ~26 degrees, but you came up with 21 (which is what I came up with). I mean, even with a conversion from radians (more accurate) to degrees (probably less accurate), I would think Mathematica would not show such a large difference in the ways this was solved. Brian On Sep 8, 2004, at 10:57 AM, David Park wrote: > Brian, > > It's often best to work with radians, but since your input is simply > stated > in degrees we'll stick with degrees. You can click in the Degree > symbol from > the Input Palette to save some typing. > > With a problem like this, it's often useful to make a plot first to > see what > is going on. > > Plot[{Cos[x =B0 + 4=B0], Sin[3x =B0 + 2=B0]}, {x, -180, 180}, > Frame -> True, > ImageSize -> 450]; > > Then NSolve gets the solutions right off. (But you have to use "==" > not "=" > in the equation.) > > NSolve[Cos[x =B0 + 4=B0] == Sin[3x =B0 + 2=B0], x] > {{x -> -159.}, {x -> -134.}, {x -> -69.}, {x -> 21.}, {x -> 46.}, {x -> > 111.}} > > You can ignore the error message in this case since the solutions > correspond > to the plot. > > If you use Ted Ersek's RootSearch package from MathSource you can > easily > obtain the roots over a wider range. > > Needs["Enhancements`RootSearch`"] > > RootSearch[Cos[x =B0 + 4=B0] == Sin[3x =B0 + 2=B0], {x, -360, 360}] > {{x -> -339.}, {x -> -314.}, {x -> -249.}, {x -> -159.}, {x -> -134.}, > {x -> -69.}, {x -> 21.}, {x -> 46.}, {x -> 111.}, > {x -> 201.}, {x -> 226.}, {x -> 291.}} > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > > From: Brian Feeny [mailto:bfeeny at mac.com] To: mathgroup at smc.vnet.net > > 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 > > > > ------------------------------------------------------------------------ ------ Brian Feeny, CCIE #8036, CISSP e: signal at shreve.net Network Engineer p: 318.213.4709 ShreveNet Inc. f: 318.221.6612

**Follow-Ups**:**Re: Re: How to solve a simple Trig cofunction?***From:*DrBob <drbob@bigfoot.com>

**Re: Exact real numbers**

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**Re: How to solve a simple Trig cofunction?**

**Re: Re: How to solve a simple Trig cofunction?**