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#1 2014-09-24 03:04:01
Trigonometric Equations
Solve for x in
tan x + 2 tan x + sqrt(3) tan x tan 2x = sqrt(3)
[latex by admin]
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#2 2014-09-24 03:57:55
- Olinguito
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- Registered: 2014-08-12
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Re: Trigonometric Equations
Bassaricyon neblina
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#3 2014-09-24 05:22:14
Re: Trigonometric Equations
Thanks 
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2014-09-24 05:29:30
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Trigonometric Equations
Have you solved that cubic and plugged in?
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.
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#5 2014-09-24 05:32:11
Re: Trigonometric Equations
I will do it later. I am busy now.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#6 2014-10-05 12:51:01
Re: Trigonometric Equations
Solve
sin(x) + cos(x) - (sin (x))^2 = 0
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#7 2014-10-05 19:33:21
- Bob
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- Registered: 2010-06-20
- Posts: 10,143
Re: Trigonometric Equations
By graphing, it looks like pi/2 is the one solution in the range 0 - 2pi. There's another that I'm tracking down now. Also working on an algebraic solution now .....
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#8 2014-10-05 19:40:43
Re: Trigonometric Equations
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#9 2014-10-05 20:05:52
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,143
Re: Trigonometric Equations
I've got 5.7083590101....
Still thinking about how to get there without trial.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#10 2014-10-05 21:38:20
Re: Trigonometric Equations
I can give a couple of complex solutions as well.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#11 2014-10-06 04:05:56
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,143
Re: Trigonometric Equations
hi,
I scribbled this out on the back of a bus ticket. It just confirms what I said earlier.
Now square both sides and you get a quartic. We can factor out the easy solution (sin(x) -1)= 0 and you're left with a cubic.
No easy factors.
Differentiating shows it has no turning points, and it goes through (0,1), so that confirms the negative solution as the only other in one [0,2pi] cycle.
As I already know it's not an simple value I think you've got to number crunch this solution.
And then, as you say, two complex solutions ... which would have to be checked against the original as squaring was involved in case they're actually solutions to
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#12 2014-10-13 02:34:34
Re: Trigonometric Equations
Solve: cos(x) - sin(3x) = cos(2x)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#13 2014-10-13 03:12:35
- Olinguito
- Member
- Registered: 2014-08-12
- Posts: 649
Re: Trigonometric Equations
Bassaricyon neblina
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#14 2014-10-13 03:38:49
Re: Trigonometric Equations
Oh thanks!
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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