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    CSCH

    Math & Trig

    Returns the hyperbolic cosecant of an angle. CSCH(x) = 1/SINH(x).

    Translations
    EnglishCSCH
    FrenchCSCH
    SpanishCSCH
    GermanCOSECHYP
    ItalianCSCH
    PortugueseCSCH
    DutchCOSECH
    PolishCSCH
    RussianCSCH
    TurkishCSCH
    CzechCOSECH
    HungarianCSCH
    SwedishCOSECH
    DanishCOSECH
    FinnishCSCH
    Syntax
    CSCH(number)

    Arguments

    • numberAny nonzero real number.
    Examples
    =CSCH(1)
    0.8509

    Hyperbolic cosecant of 1

    =CSCH(2)
    0.2757

    Hyperbolic cosecant of 2

    Tips & Best Practices
    • •Available since Excel 2013
    • •Returns #DIV/0! if number is 0
    • •CSCH(x) = 2 / (eˣ - e⁻ˣ)
    Common Mistakes
    • •Passing 0 to CSCH, which returns a #DIV/0! error since hyperbolic cosecant is undefined at zero (hyperbolic sine equals 0 at that point)
    • •Confusing CSCH with CSC - CSCH is the hyperbolic cosecant, unrelated to angles or the unit circle, while CSC is the regular trigonometric cosecant based on an angle in radians
    • •Expecting a bounded result like some other hyperbolic functions have - CSCH grows unbounded as its input approaches 0, similar to how COTH behaves near zero
    Related Functions
    SINHCalculates the hyperbolic sine, the reciprocal relationship to what CSCH calculates (CSCH(x) = 1/SINH(x)).
    SECHCalculates the hyperbolic secant, the reciprocal of hyperbolic cosine, a parallel function to CSCH's reciprocal-of-hyperbolic-sine relationship.
    CSCCalculates the regular (non-hyperbolic) cosecant of an angle, a different function despite the similar name.
    Frequently Asked Questions

    Why does CSCH return a #DIV/0! error?

    The input is 0 - hyperbolic cosecant is undefined at that point, since it's the reciprocal of hyperbolic sine, which equals 0 when the input is 0.

    Is CSCH related to angles the way CSC is?

    No, CSCH takes a plain real number, not an angle - it has no connection to radians, degrees, or the unit circle, unlike its trigonometric namesake CSC.

    Does CSCH's sign match the sign of its input?

    Yes, since hyperbolic sine is an odd function that preserves sign, its reciprocal CSCH does too - a negative input produces a negative result.

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