Question

Difference between Arctan and arctan?

Answer 1

none.

Answer 2

one with a capital A and one with a small a
no other difference

Answer 3

Really? My teacher mentioned something about it, but I don't remember it.

Answer 4

\[\text{Arctan}x=\arctan x=\tan^{-1}x\neq\tan x\]

Answer 5

Nope you're all wrong. Your teacher is smart. There is a subtle difference...Arctan(x) is an inverse function such that the range is only the principal value. However, arctan(x) takes on infinitely many values.

Answer 6

Thank you :)

Answer 7

@daksh96sharma could you please link me to a reference to what you are saying?
I'm not saying it can't be true, but I am unable to corroborate it through wolfram, mathematika, wikipedia, or any of my books.

Answer 8

AoPS Volume 2 and Beyond, Richard Rusczyk and Sandor Lehoczky. Also: http://mathworld.wolfram.com/InverseTangent.html

Answer 9

Are we satisfied?

Answer 10

" The variants Arctan z (e.g., Bronshtein and Semendyayev, 1997, p. 70) and Tan^{-1}z are sometimes used to refer to explicit principal values of the inverse cotangent, although this distinction is not always made (e.g,. Zwillinger 1995, p. 466)....Worse yet, the notation arctan z is sometimes used for the principal value, with Arctan z being used for the multivalued function (Abramowitz and Stegun 1972, p. 80"

-so yeah, I see where you are not wrong, but this is clearly not a universal notation. It is probably what the askers teacher was referring to though.