Re: How to solve a simple Trig cofunction?

*To*: mathgroup at smc.vnet.net*Subject*: [mg50530] Re: [mg50500] How to solve a simple Trig cofunction?*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 9 Sep 2004 05:18:01 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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 ° + 4°], Sin[3x ° + 2°]}, {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 ° + 4°] == Sin[3x ° + 2°], 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 ° + 4°] == Sin[3x ° + 2°], {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