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#1 2006-10-12 18:27:26

astrogirl
Member
Registered: 2006-10-12
Posts: 1

Arctan(z)

Does any one know when arctan(z) is undefined? hmm

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#2 2006-10-12 22:26:26

John E. Franklin
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Registered: 2005-08-29
Posts: 3,588

Re: Arctan(z)

I think I do, let's see, if tangent is 90 degrees, then slope is infinity.
If angle is 270 degrees then angle is -infinity, which is same as 90, sound undefined to me.


igloo myrtilles fourmis

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#3 2006-10-12 23:00:40

Dross
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Registered: 2006-08-24
Posts: 325

Re: Arctan(z)

John E. Franklin wrote:

if tangent is 90 degrees, then slope is infinity.

But the poster is asking about the arctan function. Arctan(x) is defined for every real number x.


Bad speling makes me [sic]

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#4 2006-10-13 00:28:58

John E. Franklin
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Registered: 2005-08-29
Posts: 3,588

Re: Arctan(z)

tangent of 271 degrees is -57.28 (not rounded)
tangent of 269 degrees is +57.28(not rounded)
So as you can see at 270 degrees, we don't know if it is plus or minus infinity!!
Hence it is undefined I guess!!
Also true for pi/2 (90degrees) and every  (n pi) thereafter and prior.


igloo myrtilles fourmis

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#5 2006-10-13 01:06:27

Dross
Member
Registered: 2006-08-24
Posts: 325

Re: Arctan(z)

John E. Franklin wrote:

tangent of 271 degrees is -57.28 (not rounded)
tangent of 269 degrees is +57.28(not rounded)
So as you can see at 270 degrees, we don't know if it is plus or minus infinity!!
Hence it is undefined I guess!!
Also true for pi/2 (90degrees) and every  (n pi) thereafter and prior.

You're misunderstanding - what I'm trying to say is that although the tan function is undefined at certain points, the poster is talking about the arctan function, which is entirely different, and defined everywhere on the real line.


Bad speling makes me [sic]

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#6 2006-10-13 01:43:18

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Arctan(z)

I would say that arctan(x) isn't defined at all. tan(x) = tan(x+2π), which means that every value of y is produced by multiple values of x.

Therefore, every value of arctan(x) would produce multiple values of y and so arctan(x) is not a function at any point.


Why did the vector cross the road?
It wanted to be normal.

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