Tangent zeros with a calculator?

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Discussion Overview

The discussion revolves around solving a tangent equation using a calculator, specifically focusing on the equation 3tan²x + 4tanx - 15. Participants explore the appropriate method for finding zeros and the use of a calculator in this context.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the approach for finding zeros with tangent differs from that with sine, expressing uncertainty about the variable to use in the calculator.
  • Another participant requests clarification on the specific equation, suggesting that the original post may be too vague for a technical discussion.
  • A participant suggests substituting u = tan x to simplify the equation before using the calculator, indicating that this might help in finding the values of x later.
  • Some participants emphasize the importance of analyzing the equation before relying on the calculator, suggesting that understanding the problem is crucial.
  • There is mention of the TI-89 calculator, with one participant expressing unfamiliarity with its functions and suggesting that manuals could be helpful.

Areas of Agreement / Disagreement

Participants generally agree that a calculator will be necessary for solving the equation, but there is no consensus on the best approach to take before using it. Some emphasize the need for preliminary analysis, while others focus on the calculator's role.

Contextual Notes

Participants have not resolved the specific steps for using the calculator effectively, and there are unresolved questions about the substitution and the form of the equation needed for calculation.

Tyrion101
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I'm tasked with findings he solutions to a particular tangent equation, and when I did it before with sine it was just a matter of plugging in the equation to the calculator, then getting all the zeros. Since it is tangent now and not sine, do I do something special? Is it no longer the x value anymore?
 
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Tyrion101 said:
I'm tasked with findings he solutions to a particular tangent equation, and when I did it before with sine it was just a matter of plugging in the equation to the calculator, then getting all the zeros. Since it is tangent now and not sine, do I do something special? Is it no longer the x value anymore?
This is too vague to answer. What is the equation?

Also, if this is a specific homework or textbook question, it should be posted in the Homework & Coursework section, not here in the technical math sections.
 
3tan^2x+4tanx-15, I do not want an answer but want to know as this is a standard quadratic what variable am I looking for when I punch in the zero program on my calculator. Or if I'm looking for the wrong thing entirely.
 
Tyrion101 said:
3tan^2x+4tanx-15, I do not want an answer but want to know as this is a standard quadratic what variable am I looking for when I punch in the zero program on my calculator. Or if I'm looking for the wrong thing entirely.

This appears to be a case where you are trying to let your calculator do your thinking for you. :sorry:

If you are trying to solve the equation 3tan2 x + 4tan x - 15 = 0, then a substitution of u = tan x would seem appropriate first.

Once you find out for which values of u the equation is true, then you worry about finding the values of x. :smile:
 
It's a problem where it tells me to use the calculator. In fact it states it at the very beginning of the problem. I'm unfamiliar with the ti-89.
 
Tyrion101 said:
It's a problem where it tells me to use the calculator. In fact it states it at the very beginning of the problem. I'm unfamiliar with the ti-89.
In order to find the values of u = tan x for which the equation is true, yes, I agree that a calculator will be necessary. But my point was that you are trying to apply the calculator before you have finished analyzing the equation, to put it into a form amenable for finding a solution with the calculator.

There are sites online where you can download a manual for the TI-89 and which can probably show you how to use its various functions to solve your equation.
 
SteamKing said:
In order to find the values of u = tan x for which the equation is true, yes, I agree that a calculator will be necessary. But my point was that you are trying to apply the calculator before you have finished analyzing the equation, to put it into a form amenable for finding a solution with the calculator.
I strongly agree. Think first, then use a calculator.
 

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