How to get (secx)(tanx) from (1/cosx)(sinx/cosx)?

  • Context: High School 
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Discussion Overview

The discussion revolves around the transformation of the function h(x) = sin(x)/cos²(x) into the form (sec(x))(tan(x)). Participants explore the steps involved in this transformation and the implications for finding antiderivatives.

Discussion Character

  • Technical explanation
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to derive (sec(x))(tan(x)) from the given function h(x).
  • Another participant clarifies that 1/cos(x) is sec(x) and sin(x)/cos(x) is tan(x), suggesting a simplification.
  • A participant proposes that the answer could be (sec(x))(tan(x)) + c, questioning if this is correct.
  • One participant notes that the transformation is a simplification and emphasizes the need to clarify whether the goal is to find the antiderivative.
  • Another participant suggests finding the function with a derivative of sec(x)tan(x) and references a list of such facts in textbooks.
  • A later reply indicates that understanding the goal of finding an antiderivative would have clarified the discussion from the start.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the overall goal of the discussion, with some focusing on the transformation and others on the antiderivative aspect. Confusion remains regarding the initial problem statement and its requirements.

Contextual Notes

There is a lack of clarity regarding the original problem statement and whether the transformation is intended for simplification or for finding an antiderivative. Assumptions about the context of the problem are not fully articulated.

helpm3pl3ase
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Quick question:

h(x) = sinx/cos^(2) x

= (1/cosx)(sinx/cosx)

Then you get (secx)(tanx)..

I do not get how they get secx x tanx?? Anyone?? Thanks
 
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1/cos(x) is also called sec(x).

sin(x)/cos(x) is also called tan(x).

- Warren
 
so the answer would be

(secx)(tanx) + c

Correct??
 
All you've done so far is convert the function you gave me into a slightly simpler form.

sin(x) / cos^2(x) = sec(x) tan(x).

Since you didn't actually post the problem as it was given to you, I don't know if h(x) is a function of which you need to find the antiderivative, or whether you've already done that step. You probably need to actually perform the antiderivative now.

- Warren
 
sorry how would i go about doing this.. Iam so confused.
 
Find the function which has a derivative of sec(x) tan(x). You should have a list of such facts in your book.

- Warren
 
alright.. I get it now.. Sorry.. I don't know why this problem was causing me problems.. Thanks for clearing it up.
 
Do you know the method of substitution to find antiderivatives ? If so, just plug

[tex]\cos x = t[/tex]

and c what u get.

Daniel.
 
It would have helped if you had told us from the beginning that you were trying to find an anti-derivative! All you said was that you couldn't see how they had gone from Quick question:

h(x) = sinx/cos^(2) x

to h(x)= (secx)(tanx).
 

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