ACOSH
Returns the inverse hyperbolic cosine of a number. The argument must be greater than or equal to 1.
ACOSH(number)Arguments
numberAny real number greater than or equal to 1.
=ACOSH(1)ACOSH of 1 is 0
=ACOSH(10)Inverse hyperbolic cosine of 10
- •Returns #NUM! if number < 1
- •ACOSH is the inverse of COSH: ACOSH(COSH(x)) = x for x ≥ 0
- •Result is in radians, not degrees
- •Passing a number less than 1, which returns a #NUM! error since the inverse hyperbolic cosine is only defined for inputs of 1 or greater
- •Confusing ACOSH with ACOS - ACOSH works with hyperbolic cosine values (which range from 1 to infinity), while ACOS works with regular trigonometric cosine values (which range from -1 to 1)
- •Expecting the result to be in degrees - like other inverse hyperbolic and trigonometric functions in Excel, ACOSH's result is a dimensionless value, not an angle in radians or degrees the way ACOS's result is
COSHPerforms the inverse operation - calculates the hyperbolic cosine of a number, undoing what ACOSH calculates.ASINHCalculates the inverse hyperbolic sine, a related function defined for all real numbers rather than ACOSH's restricted domain of 1 and above.ACOSCalculates the regular (non-hyperbolic) inverse cosine, a different function despite the similar name, with a completely different valid input range.Why does ACOSH return a #NUM! error?
The input is less than 1 - the inverse hyperbolic cosine is only mathematically defined for numbers greater than or equal to 1.
What's the difference between ACOSH and ACOS?
They're unrelated despite the similar name - ACOSH is the inverse hyperbolic cosine, valid for inputs of 1 or greater, while ACOS is the regular inverse cosine, valid only for inputs between -1 and 1.
How do I verify ACOSH's calculation manually?
ACOSH(x) equals COSH's inverse, so COSH(ACOSH(x)) should return x - useful for double-checking a result or understanding the relationship between the two functions.
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