Syntax
COSH(number)
| Parameter | Description |
|---|---|
| number | Parameter of the COSH function. |
Examples
COSH of 0
Formula
=COSH(0)
Returns 1. The minimum value of COSH is 1, occurring at x=0. Unlike COS which oscillates, COSH only increases from this minimum.
COSH of 1
Formula
=COSH(1)
Returns ~1.5431. The hyperbolic cosine of 1 is (e¹ + e⁻¹)/2 ≈ 1.5431.
Catenary curve
Formula
=100*COSH(A1/100)-100
Models the sag of a cable spanning a distance, where A1 is the horizontal position from center. The shape is a catenary, not a parabola.
Common Errors
#VALUE!
Non-numeric input returns #VALUE!.
#NUM!
Very large inputs cause overflow. COSH(710) is approximately the limit before #NUM!.
Tips
Always >= 1
COSH(x) is always at least 1 for any real x. Its minimum is COSH(0) = 1, and it grows exponentially in both directions.
Catenary vs parabola
A hanging cable forms a catenary (COSH curve), not a parabola. For short spans the difference is small, but for long spans like power lines, the catenary model is more accurate.
Even function
COSH(-x) = COSH(x). It's symmetric, which makes sense since (e^x + e^(-x))/2 doesn't change when you negate x.
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