Math Is Fun Forum

mp3qz

Member

Registered: 2009-07-21

Posts: 9

trig equation

juriguen

Member

Registered: 2009-07-05

Posts: 59

Re: trig equation

Hi

I would do the following:

Using sin(x) = z

If I did the calculations correctly, reordering and solving first for z and then for x, you should obtain the answer directly given by the quickmath website:

Jose

(Edited, since I didn't write the last equation correctly!)

Last edited by juriguen (2009-07-23 18:52:29)

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“Make everything as simple as possible, but not simpler.” -- Albert Einstein

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: trig equation

Hi mp3qz;

There are an infinite number of roots. For the real roots the solution set is.

Last edited by bobbym (2009-07-22 04:54:17)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mp3qz

Member

Registered: 2009-07-21

Posts: 9

Re: trig equation

juriguen, z=?? or an exact result for x

Last edited by mp3qz (2009-07-23 16:19:32)

juriguen

Member

Registered: 2009-07-05

Posts: 59

Re: trig equation

Hi again!

The exact solutions are really long to type, but you can easily find them using:
http://www.quickmath.com/webMathematica3/quickmath/page.jsp?s1=equations&s2=solve&s3=advanced

Just type
1/4 + 4*z + 17*z^2 + 8*z^3 + z^4 = 3*z^2 *(1-z^2)
in the equations box

and z in the variables box. Then click solve!

If you want the result for x, use the original equation directly.

By the way, bobbym is right extending the real solutions + 2 pi n. What about the complex solutions?

Jose

Last edited by juriguen (2009-07-23 19:00:44)

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“Make everything as simple as possible, but not simpler.” -- Albert Einstein

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: trig equation

Hi

Complex roots achieved by iteration with newtons method to the complex plane.

The values 2.69...,1.278...,2.89...,.0888..., could not be expressed in simple terms.

Last edited by bobbym (2009-07-24 02:05:45)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.