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)
• 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
>>
>> 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

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