SECH
Returns the hyperbolic secant of an angle. SECH(x) = 1/COSH(x).
SECH(number)Arguments
numberAny real number.
=SECH(0)SECH(0) is always 1
=SECH(2)Hyperbolic secant of 2
- •Available since Excel 2013
- •Result is always strictly between 0 and 1
- •SECH(x) = 2 / (eˣ + e⁻ˣ)
- •Confusing SECH with SEC - SECH is the hyperbolic secant, unrelated to angles or the unit circle, while SEC is the regular trigonometric secant based on an angle in radians
- •Expecting SECH to grow toward infinity for large inputs the way SEC can - SECH actually shrinks toward 0 as the input grows larger in either direction, the opposite of an unbounded growth pattern
- •Assuming SECH's output could be negative - since it's the reciprocal of hyperbolic cosine (which is always positive), SECH's result is always strictly between 0 and 1
COSHCalculates the hyperbolic cosine, the reciprocal relationship to what SECH calculates (SECH(x) = 1/COSH(x)).CSCHCalculates the hyperbolic cosecant, the reciprocal of hyperbolic sine, a parallel function to SECH's reciprocal-of-hyperbolic-cosine relationship.SECCalculates the regular (non-hyperbolic) secant of an angle, a different function despite the similar name.What's the difference between SECH and SEC?
They're unrelated despite the similar name - SECH is the hyperbolic secant, always between 0 and 1 and taking any real number as input, while SEC is the regular trigonometric secant, which can produce very large values and interprets its input as an angle in radians.
Does SECH ever return a negative number?
No, since it's the reciprocal of hyperbolic cosine (which is always 1 or greater), SECH's result is always positive, strictly between 0 and 1.
What happens to SECH for very large inputs?
It shrinks toward 0 - as the input grows larger in either the positive or negative direction, hyperbolic cosine grows toward infinity, so its reciprocal shrinks toward 0.
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