Syntax
SECH(number)
| Parameter | Description |
|---|---|
| number | Parameter of the SECH function. |
Examples
SECH of 0
Formula
=SECH(0)
Returns 1. The maximum value of SECH occurs at 0, where 1/COSH(0) = 1/1 = 1.
SECH of 1
Formula
=SECH(1)
Returns ~0.6481. SECH decreases from its peak of 1 as |x| increases.
Pulse shape
Formula
=SECH(A1/2)^2
SECH² is the shape of a soliton (solitary wave). It models laser pulse shapes and water wave packets.
Common Errors
#VALUE!
Non-numeric arguments return #VALUE!.
Tips
Bell-shaped curve
SECH produces a bell curve similar to the Gaussian but with heavier tails. It's the hyperbolic analog of the cosine wave's shape.
Always positive
SECH(x) is always positive, between 0 and 1. It equals 1 at x=0 and approaches 0 as |x| increases.
Even function
SECH(-x) = SECH(x). The curve is symmetric about the y-axis, just like COSH.
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