Cot and Arctan: Understanding the Difference

[JeeebeZ]

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)?

 

[w4k4b4lool4]

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 ..

 

[uart]

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.

 

[uart]

BTW. arc_cot(x) does equal arc_tan(1/x), so perhaps that is what you were thinking?

 

[JeeebeZ]

Nope I did it wrong...

I went from 1 + tan²A = tan²A

instead of going from 1 + tan²A = sec²A

Which messed up my entire question.