Cot and Arctan: Understanding the Difference

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SUMMARY

The discussion clarifies the distinction between the cotangent and arctangent functions, specifically addressing the misconception that -11 cot(1/x + 2) is equivalent to 11 arctan(x + 2). Participants confirm that cotangent and arctangent are fundamentally different functions. Additionally, the discussion highlights a common error among students regarding the manipulation of inverse functions and their reciprocals, emphasizing that arc_cot(x) equals arc_tan(1/x), which may have contributed to the confusion.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cotangent and arctangent.
  • Familiarity with inverse functions and their properties.
  • Basic algebraic manipulation skills.
  • Knowledge of the Pythagorean identity related to trigonometric functions.
NEXT STEPS
  • Study the properties of cotangent and arctangent functions in detail.
  • Learn about the relationship between inverse functions and their reciprocals.
  • Review the Pythagorean identities in trigonometry.
  • Practice problems involving the manipulation of trigonometric identities and equations.
USEFUL FOR

Students of mathematics, particularly those studying trigonometry and calculus, as well as educators looking to clarify common misconceptions about trigonometric functions.

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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