Python Hyperbolic Functions

Hyperbolic functions are analogs of trigonometric functions that are based on the hyperbola rather than the circle.

acosh() Function

The acosh() function returns the inverse hyperbolic cosine of x.

Syntax

math.acosh(x)

Parameters

• x – A positive number greater than or equal to 1.

Return Value

This function returns a floating-point number corresponding to the inverse hyperbolic cosine of x.

Example

from math import acosh

x = 30
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 5.5
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 1
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 0.5
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

x = 45
val = acosh(x)
print ("x: ",x, "acosh(x): ", val)

It will produce the following Output −

x: 30 acosh(x): 4.0940666686320855
x: 5.5 acosh(x): 2.389526434574219
x: 1 acosh(x): 0.0
Traceback (most recent call last):
File “C:Usersmlathexamplesmain.py”, line 17, in
val = acosh(x)
^^^^^^^^
ValueError: math domain error

asinh() Function

The asinh() function returns the inverse hyperbolic sine of a given positive or negative number.

Syntax

math.asinh(x)

Parameters

• x – A positive or negative number.

Return Value

The asinh() function returns a floating-point number representing the inverse hyperbolic sine of x.

Example

from math import asinh

x = 24
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

x = -12
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

x = 1
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

x = 0.5
val = asinh(x)
print ("x: ",x, "asinh(x): ", val)

This will produce the following output −

x: 24 asinh(x): 3.8716347563877314
x: -12 asinh(x): -3.179785437699879
x: 1 asinh(x): 0.881373587019543
x: 0.5 asinh(x): 0.48121182505960347

atanh() Function

The atanh() function in the math module returns the inverse hyperbolic tangent of a number.

Syntax

math.tanh(x)

Parameters

• x – The numeric operand for which the inverse hyperbolic tangent is to be calculated. Must be in the range -0.99 to 0.99.

Return Value

The atanh() function returns the inverse hyperbolic tangent of x.

Example

from math import atanh

x = 0.55
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

x = -0.55
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

x = 0
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

x = 1.25
val = atanh(x)
print ("x: ",x, "atanh(x): ", val)

This will produce the following output: −

x: 0.55 atanh(x): 0.6183813135744636
x: -0.55 atanh(x): -0.6183813135744636
x: 0 atanh(x): 0.0
Traceback (most recent call last):
File "C:Usersmlathexamplesmain.py", line 17, in
val = atanh(x)
^^^^^^^^
ValueError: math domain error

cosh() Function

The cosh() function is a function in the math module that returns the hyperbolic cosine of a given number. This value is equal to (exp(x) + exp(-x)) / 2.

Syntax

math.cosh(x)

Parameters

• x – The number whose hyperbolic cosine is to be calculated.

Return Value

The cos() function returns a floating-point number representing the hyperbolic cosine of x.

Example

from math import cosh

x = 0.55
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

x = 1
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

x = 0
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

x = 6.50
val = cosh(x)
print ("x: ",x, "cosh(x): ", val)

This will produce the following output −

x: 0.55 cosh(x): 1.155101414123941
x: 1 cosh(x): 1.5430806348152437
x: 0 cosh(x): 1.0
x: 6.5 cosh(x): 332.5715682417774

sinh() Function

The sinh() function returns the hyperbolic sine of a given number.

Syntax

math.sinh(x)

Parameters

• x – The number whose sinh is to be calculated.

Return Value

The sinh() function returns the hyperbolic sine of x as a double-precision floating-point number.

Example

from math import sinh, pi

x = 1
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x = 12.23
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x = -12.23
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x = 0
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

x=pi
val = sinh(x)
print ("x: ",x, "sinh(x): ", val)

It will produce the following Output –

x: 1 sinh(x): 1.1752011936438014
x: 12.23 sinh(x): 102421.59104557337
x: -12.23 sinh(x): -102421.59104557337
x: 0 sinh(x): 0.0
x: 3.141592653589793 sinh(x): 11.548739357257746

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tanh() Function

The tanh() function in the math module returns the hyperbolic tangent of a given number.

Syntax

math.tanh(x)

Parameters

• x – The number to calculate the hyperbolic tangent.

Return Value

The tanh() function returns a floating-point number representing the hyperbolic tangent of the argument x.

Example

from math import tanh, pi

x = 1
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = 12.23
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = -12.23
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = 0
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

x = pi
val = tanh(x)
print ("x: ",x, "tanh(x): ", val)

This will produce the following Output −

x: 1 tanh(x): 0.7615941559557649
x: 12.23 tanh(x): 0.9999999999523363
x: -12.23 tanh(x): -0.9999999999523363
x: 0 tanh(x): 0.0
x: 3.141592653589793 tanh(x): 0.99627207622075