What is "Z" - Alphas, LaTex & MathType Explored

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Discussion Overview

The discussion revolves around the mathematical exploration of a question involving the existence of certain pairs of alphas in relation to the tangent function and their sum equating to a specific value. The conversation touches on the use of LaTeX and MathType for mathematical expressions.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant expresses a desire to learn LaTeX while being familiar with MathType, questioning the existence of pairs of alphas.
  • Another participant suggests that the question simplifies to whether there exist alphas in the rational numbers such that their tangents sum to π/3, but expresses uncertainty about the answer.
  • A third participant questions whether the function in the original question is indeed tangent or arctangent, noting a lack of known identities involving arctangent and multiples of π.
  • A fourth participant proposes a specific value for α1 as a potential solution to the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are differing interpretations of the mathematical question and uncertainty about the existence of the proposed pairs of alphas.

Contextual Notes

There are unresolved assumptions regarding the definitions of the functions involved and the conditions under which the proposed mathematical relationships hold.

bomba923
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I wish I knew LaTex :frown: . But I know MathType!

Does such a pair of alphas exist?? (See the Below Thumbnail/attached image)
"Z" is the set of all integers
 

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LaTeX is really easy to learn, just click on stuff people have wrote and it will show you the code. Check this thread out: https://www.physicsforums.com/showthread.php?t=8997

Correct me if I am wrong but your question simplifies down to:

[tex]\text{If} \, \alpha_1 \in \mathbb{Q} \, \, \, \text{does} \, \exists \, \alpha_2 \in \mathbb{Q}[/tex]

Such that:

[tex]\tan \left( \alpha_1 \right) + \tan \left( \alpha_2 \right) = \frac{\pi}{3}[/tex]

I'd guess not but to be honest I have no idea.

Oh and I think the question is wrong otherwise you could always let k=0.
 
Last edited:
Are we sure that that is supposed to be a tangent and not an arctangent ? I don't know of any "special" identities involving the arctangent of multiples of pi. The term in pi looks more suited to be the argument of the tangent function.
 
Let [itex]\alpha_1 = 1^c[/itex]

That should solve the problem.
 

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