Is there a mathematical symbol for expressing one function in terms of another?

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Discussion Overview

The discussion revolves around the question of whether there is a mathematical symbol that expresses the concept of one function being represented "in terms of" another function. The context includes a specific example involving trigonometric functions and identities.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about a mathematical symbol for expressing one function in terms of another, using the example of cos(x) / tan(x) in terms of sin(x).
  • Another participant suggests that there is no specific symbol for the phrase "in terms of," indicating that it is typically written out.
  • It is noted that the lack of a symbol is why the phrase is often explicitly stated as "In terms of...".
  • A participant emphasizes the need to use trigonometric identities to convert functions into forms that utilize only sin(x), suggesting that the exercise should be designed to allow such conversions.
  • A later reply reiterates the participant's understanding of the solution to the example problem, while also expressing curiosity about the existence of a mathematical construct for the phrase "in terms of".

Areas of Agreement / Disagreement

Participants generally agree that there is no established symbol for expressing "in terms of," but there is no consensus on the necessity or utility of such a symbol.

Contextual Notes

The discussion does not resolve whether a symbol could be beneficial or if the phrase's explicit use is sufficient for clarity in mathematical communication.

nanoWatt
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math symbol for "in terms of"

If there was a simple trig problem like express cos(x) / tan(x) in terms of sin(x).

I can't seem to find the mathematical symbol for doing "in terms of". I'm learning on my own, and don't yet have my calculus book, so I'm just reviewing sample problems, but they just say "in terms of" without any symbols.

I know the answer is 1/sin(x) - sin(x)

But for myself, I'm just wondering.
 
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I don't think there is a symbol for that phrase.
 
Apparently they lack a symbol, that's why the write it out: "In terms of.."
 
You need to make use of identities to convert all functions into equivalent forms using only sin(x). Your exercise problem should already be designed for this to be possible.
Do you have a specific exercise as an example?
 
I pretty much know the answer:

cos(x) / tan(x) in terms of sin(x) = 1/sin(x) - sin(x)

I didn't need help solving it. I just wondered if there was a mathematical construct for in terms of.

symbolipoint said:
You need to make use of identities to convert all functions into equivalent forms using only sin(x). Your exercise problem should already be designed for this to be possible.
Do you have a specific exercise as an example?
 

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