Hyperbolic Functions
Hyperbolic functions are analogs of trigonometric functions that are based on hyperbolas instead of circles.
acosh() Function
The acosh() function returns inverse hyperbolic cosine of x.
Syntax
math.acosh(x)
Parameters
x − A positive number >= 1.
Return Value
This function returns a float, corresponding to 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:\Users\mlath\examples\main.py", line 17, in <module>
val = acosh(x)
^^^^^^^^
ValueError: math domain error
asinh() Function
The asinh() function returns the inverse hyperbolic sine value of a positive or negative number.
Syntax
math.asinh(x)
Parameters
x − a positive or negative number.
Return Value
The asinh() function returns a float that represents 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)
It 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 math module returns the inverse hyperbolic tangent of a number.
Syntax
math.tanh(x)
Parameters
x − a numeric operand for which atanh value 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)
It 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:\Users\mlath\examples\main.py", line 17, inval = atanh(x) ^^^^^^^^ ValueError: math domain error
cosh() Function
The cosh() function in math module returns the hyperbolic cosine value of the given number. The value is equivalent to (exp(x) + exp(-x)) / 2.
Syntax
math.cosh(x)
Parameters
x − a number whose hyperbolic cosine is to be found.
Return Value
The cosh() function returns a float, 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)
It 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 given number.
Syntax
math.sinh(x)
Parameters
x − a number whose sinh value is to be computed.
Return Value
The sinh() function returns a float representing the hyperbolic sine of x.
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
tanh() Function
The tanh() function in math module returns the hyperbolic tangent of a given number.
Syntax
math.tanh(x)
Parameters
x − a number to calculate the hyperbolic tangent.
Return Value
The tanh() function returns a float number and represents the hyperbolic tangent value of 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)
It 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