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

*To*: mathgroup at smc.vnet.net*Subject*: [mg50561] Re: [mg50519] Re: [mg50500] How to solve a simple Trig cofunction?*From*: George Woodrow III <georgevw3 at mac.com>*Date*: Fri, 10 Sep 2004 04:06:02 -0400 (EDT)*References*: <200409080914.FAA08518@smc.vnet.net> <913EB31F-018F-11D9-8C24-000A95B4967A@akikoz.net> <200409090917.FAA19326@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In the equation, 4 and 5 are in radians. If you want to solve the equation with everything in degrees, you need to enter 4 as 4 Degree, etc. george On 9 Sep, 2004, at 5:17 am, Brian Feeny wrote: > > On Sep 8, 2004, at 7:06 AM, Andrzej Kozlowski wrote: > >> I have no idea what a "Trig cofunction" is ;-) >> >> Mathematica can solve this exactly (so there is no need to use >> numerical methods, and in any case NSolve would be the wrong solver to >> use since it does not deal with trig equations) >> >> This gives the exact answer in radians: >> >> > > > Thanks for replying. The correct numerical answer is 21degrees > however, I wonder why the numerical > answers below are 5 degrees too much? > > You have given me alot to think about in ways to use Mathematica and I > will read in the manual further to try > to make sense of it, thanks. > > Brian > > > > > >> Reduce[{Cos[x + 4] == Sin[3*x + 2], 0 < x < Pi}, x] >> >> >> x == 1 - 2*ArcTan[1 - Sqrt[2]] || >> x == (1/2)*(-3 + 2*Pi - 2*ArcTan[1 - Sqrt[2]]) || >> x == (1/2)*(-3 + 2*Pi - 2*ArcTan[1 + Sqrt[2]]) >> >> If you prefer an answer in degrees you get do this: >> >> >> (x /. {ToRules[Reduce[{Cos[x + 4] == Sin[3*x + 2], >> 0 < x < Pi}, x]]})*(180/Pi) >> >> {(180*(1 - 2*ArcTan[1 - Sqrt[2]]))/Pi, >> (90*(-3 + 2*Pi - 2*ArcTan[1 - Sqrt[2]]))/Pi, >> (90*(-3 + 2*Pi - 2*ArcTan[1 + Sqrt[2]]))/Pi} >> >> And if you prefer a numerical answer you can just apply N: >> >> >> N[%] >> >> >> {102.296,116.556,26.5563} >> >> >> Andrzej Kozlowski >> >> Chiba, Japan >> http://www.akikoz.net/~andrzej/ >> http://www.mimuw.edu.pl/~akoz/ >> > > --Apple-Mail-2-375055142 > content-disposition: inline; filename=PGP.sig > > -----BEGIN PGP SIGNATURE----- > Version: GnuPG v1.2.4 (Darwin) > > iD8DBQFBPvpkTAQugQFRj8MRAuhSAJ9A/NzsYPApDJ9y1yj2wldlyGOGWACgkhCu > ++66pwBvW8z2b6w+Zp7MWb4= > =kGek > -----END PGP SIGNATURE----- > > --Apple-Mail-2-375055142-- >

**References**:**How to solve a simple Trig cofunction?***From:*bfeeny@mac.com (Brian Feeny)

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