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Math function
SECH
Returns the hyperbolic secant of a number.
Rarely usedDifficulty 1350 · AdvancedUsage rank #331 of 520
When to use it
Hyperbolic secant: 1/COSH. A bell-shaped curve that is never zero.
The shape of it
- Syntax
=SECH(number)
Worked examples
Zero
=SECH(0) → 1
The peak.
One
=SECH(1) → 0.648054274
One.
Negative
=SECH(-2) → 0.265802229
Even function, so the same as SECH(2).
Worth knowing
- Appears in soliton and pulse-shape formulas.
- SECH(x) = 1/COSH(x).
- No direct inverse; use ACOSH(1/x).
Where it goes wrong
- Never errors for real input, but underflows to 0 for large values.
- Not an angle function.
Related
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