Syntax
ACOTH(number)
| Parameter | Description |
|---|---|
| number | Parameter of the ACOTH function. |
Examples
ACOTH of 2
Formula
=ACOTH(2)
Returns ~0.5493. This is 0.5 × LN(3/1) = 0.5 × LN(3) ≈ 0.5493.
ACOTH of 5
Formula
=ACOTH(5)
Returns ~0.2027. As the input grows larger, ACOTH approaches 0.
Verify inverse
Formula
=COTH(ACOTH(3))
Returns 3. Confirms that ACOTH is the inverse function of COTH.
Common Errors
#NUM!
The argument must satisfy |x| > 1. =ACOTH(0.5), =ACOTH(1), and =ACOTH(-1) all return #NUM! because the function is undefined there.
#VALUE!
Non-numeric input returns #VALUE!.
Tips
Domain restriction
ACOTH only accepts x > 1 or x < -1. The interval [-1, 1] is not in the domain. This is the opposite of ATANH, which requires |x| < 1.
Logarithmic formula
ACOTH(x) = 0.5 × LN((x+1)/(x-1)). If your spreadsheet doesn't have ACOTH, you can compute it from LN.
Related to ATANH
ACOTH(x) = ATANH(1/x). They are closely related — ACOTH operates outside [-1,1] while ATANH operates inside.
Try ACOTH in Viztab
Import your data and use ACOTH with 370+ other formulas. No signup required.
Open Viztab