acsch(): The Inverse Hyperbolic Cosecant

acsch() reverses csch(), the reciprocal hyperbolic sine. It is useful in symbolic work and models expressed through hyperbolic reciprocals, including some integrals and solutions of differential equations.

Input restrictions

For real arithmetic, acsch(x) accepts every nonzero real x. Zero is excluded because csch itself is never zero and has a singularity there. Positive inputs produce positive outputs, while negative inputs produce negative outputs; this odd symmetry is a helpful sanity check.

An equivalent form is asinh(1/x), connecting acsch to asinh(). That identity also highlights the practical caveat: dividing by a very small number creates a large magnitude. Check for zero and decide how near-zero measurements should be handled before evaluating.

Using and checking acsch

Apply csch(acsch(x)) to recover x, subject to floating-point precision. Pair it with sinh() when converting between reciprocal and direct hyperbolic forms, and use log() only when you need to derive or inspect an equivalent expression.

Although its name resembles acsc, acsch belongs to the hyperbolic family, not circular trigonometry. Keep those families separate when selecting identities and interpreting units.