Math & Trig

SECH Formula

SECH returns the hyperbolic secant of a number, defined as 1/COSH(x) or 2/(e^x + e^(-x)). It produces a bell-shaped curve centered at 0 with a maximum value of 1. SECH appears in soliton theory, pulse shape modeling, and certain distribution functions in physics.

Syntax

SECH(number)
ParameterDescription
number Parameter of the SECH function.
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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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