Cot and Arctan: Understanding the Difference

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Homework Help Overview

The discussion revolves around the relationship between cotangent and arctangent functions, specifically questioning whether -cot(1/x + 2) is equivalent to arctan(x + 2). Participants are examining the differences between these trigonometric functions and their inverses.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the equivalence of cotangent and arctangent functions, with some expressing confusion over the manipulation of these functions. There is an exploration of the implications of dropping terms in equations and the distinction between inverse functions and reciprocals.

Discussion Status

The discussion includes various perspectives on the relationship between cotangent and arctangent, with some participants providing clarifications on the differences. There is acknowledgment of common misconceptions among students regarding these functions. A suggestion to post working steps has been made to further clarify the confusion.

Contextual Notes

Participants are navigating through potential misunderstandings related to trigonometric identities and the manipulation of equations. There is mention of a mistake in applying a trigonometric identity, which has impacted the original question.

JeeebeZ
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I got a answer of

-11 cot ( 1 / x + 2 )

the text shews the answer as

11 arctan ( x + 2 )

is this the same thing?

meaning

-cot(1/x) = arctan(x)?
 
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JeeebeZ said:
I got a answer of

-11 cot ( 1 / x + 2 )

the text shews the answer as

11 arctan ( x + 2 )

is this the same thing?

meaning

-cot(1/x) = arctan(x)?

No, these two are not the same ..
Also, even if they were, the latter equality you write down wouldn't follow from the former equality because you can't just drop the 2 ..
 
JeeebeZ said:
I got a answer of

-11 cot ( 1 / x + 2 )

the text shews the answer as

11 arctan ( x + 2 )

is this the same thing?

meaning

-cot(1/x) = arctan(x)?

No, cot and arctan are completely different functions JeeebeZ.

Why don't you post your working. It looks like you may be confusing inverse functions with reciprocals, which is very wrong, but not all that an uncommon mistake for students who are just starting out with manipulating functions.
 
BTW. arc_cot(x) does equal arc_tan(1/x), so perhaps that is what you were thinking?
 
Nope I did it wrong...

I went from 1 + tan2A = tan2A

instead of going from 1 + tan2A = sec2A

Which messed up my entire question.
 

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