ACOSH()

Syntax. ACOSH(number)

Definition. This function returns the inverse hyperbolic cosine of a number (see Figure 16-3). The definition range spans x = +1 to + ∞.

Argument

• number (required) A real number equal to or greater than 1.

Background. The inverse hyperbolic functions are also called the area hyperbolic functions. They are the inverse functions of the hyperbolic functions. The hyperbolic functions sinh, tanh, and coth are strictly monotonic and have one inverse function. The cosh function, however, has two monotonic intervals symmetrical to the positive segment of the ordinate and two inverse functions:

y = arcosh x

and

y = -arcosh x

where:

The graph (see Figure 16-3) starts at point 1.0 and is monotone increasing or decreasing.

Note

Inverse hyperbolic functions have the prefix ar in the same way that the inverse trigonometric functions have the prefix arc. The notations sinh^–1, cosh^–1, or tanh^–1 are also used.

Figure 16-3. The graph of the arcosh shows the monotonic increasing segment in the first quadrant. The monotonic decreasing segment is located inversely under the abscissa.

Example. Two parallel wires with the diameter d, length l, and distance a have the capacitance C.

ε = ε₀ ε_r is the permittivity of the medium.

More examples of this function are:

• =ACOSH(1) returns 0.

• =ACOSH(2) returns 1.3169579.

• =ACOSH(8) returns 2.76865938.

See Also

ASINH(), ATANH(), COSH(), SINH(), TANH()

Sample Files

Use the Data&Chart and Example worksheets in the ACosH.xls or ACosH.xlsx sample file. The sample files are found in the Chapter16 folder. For more information about the sample files, see the section titled Using the Sample Files.