ATANH()

Syntax. ATANH(number)

Definition. This function returns the inverse hyperbolic tangent of a number (see Figure 16-9). The number must be between –1 and 1.

Argument

• number (required) Any real number between –1 and 1

Background. The inverse hyperbolic functions are the inverse functions of the hyperbolic functions. The formula for the inverse hyperbolic tangent is:

Note

Inverse hyperbolic functions have the prefix ar in the same way that the inverse trigonometric functions have the prefix arc.

Figure 16-9. The function is odd and is defined only for –1 < x < 1.

Examples. Examples of this function are:

• =ATANH(0) returns 0.

• =ATANH(0.5) returns 0.54930614.

• =ATANH(-0.5) returns -0.54930614.

• =ATANH(0.999) returns 3.80020117.

• =ATANH(-0.999) returns -3.80020117.

See Also

ACOSH(), ASINH(), COSH(), SINH(), TANH()

Sample Files

Use the Data&Chart worksheet in the ATanH.xls or ATanH.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.