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

*To*: mathgroup at smc.vnet.net*Subject*: [mg50574] Re: [mg50532] Re: [mg50500] How to solve a simple Trig cofunction?*From*: DrBob <drbob at bigfoot.com>*Date*: Fri, 10 Sep 2004 04:06:49 -0400 (EDT)*References*: <NDBBJGNHKLMPLILOIPPOGENGECAA.djmp@earthlink.net> <200409090918.FAA19403@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

I added 4 radians rather than 4 degrees on the left hand side, and similarly on the right. Bobby On Thu, 9 Sep 2004 05:18:10 -0400 (EDT), Brian Feeny <bfeeny at mac.com> wrote: > 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 > 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 > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Re: How to solve a simple Trig cofunction?***From:*Brian Feeny <bfeeny@mac.com>