Syntax
COTH(number)
| Parameter | Description |
|---|---|
| number | Parameter of the COTH function. |
Examples
COTH of 1
Formula
=COTH(1)
Returns ~1.3130. The hyperbolic cotangent of 1 is COSH(1)/SINH(1) ≈ 1.5431/1.1752 ≈ 1.3130.
COTH of 2
Formula
=COTH(2)
Returns ~1.0373. COTH approaches 1 as its argument increases.
Verify with TANH
Formula
=COTH(3) - 1/TANH(3)
Returns 0 (or very near 0). Confirms that COTH(x) = 1/TANH(x).
Common Errors
#DIV/0!
COTH(0) is undefined because SINH(0) = 0, making the division impossible.
#VALUE!
Non-numeric arguments return #VALUE!.
Tips
1/TANH shorthand
COTH(x) = 1/TANH(x). If your spreadsheet doesn't have COTH, use the reciprocal of TANH instead.
Undefined at zero
COTH has a vertical asymptote at x=0. The function goes to +∞ from the right and -∞ from the left.
Approaches ±1
For large positive x, COTH(x) → 1. For large negative x, COTH(x) → -1. It converges much faster than COT, which oscillates.
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