This example illustrates how to apply inverse (arc) hyperbolic functions to your transformations.

Source:

In the following sample, input values are in radians. In this example, all values are rounded to two decimals for clarity.


Y
-4.00
-3.00
-2.00
-1.00
-0.75
-0.50
0.00
0.50
0.75
1.00
2.00
3.00
4.00

Transformation:

The following transformations include checks for the valid ranges for input values.

Hyperbolic arcsine:

Hyperbolic arccosine: 

Valid over the range (y > 1)

Hyperbolic arctangent: 

Valid over the range (-1 < y < 1)

Results:

YatanhYacoshYasinhY
-4nullnull-120.02
-3nullnull-104.19
-2nullnull-82.71
-1.5nullnull-68.45
-1nullnull-50.5
-0.75-55.75null-39.71
-0.5-31.47null-27.57
00null0
0.531.47null27.57
0.7555.75null39.71
1nullnull50.5
1.5null55.1468.45
2null75.4682.71
3null101104.19
4null118.23120.02