Python math.acosh() Method

1. Syntax of Python math.acosh() Method
2. Example Codes: Use Python math.acosh() to Compute Inverse Hyperbolic Cosine of a Value
3. Example Codes: Use Python math.acosh() to Compute Arccosine and Cosine

Python has a built-in library named math for performing many mathematical operations. Fortunately, this library also supports trigonometric and inverse trigonometric operations.

The inverse of a hyperbolic cosine is known as inverse hyperbolic cosine or cosh⁻¹θ. Its domain is the closed interval [1, +∞).

arcosh(θ) = ln(θ + √(θ² - 1))

This article will discuss the acosh() method from the math module that helps compute inverse hyperbolic cosine for angles.

Syntax of Python math.acosh() Method

math.acosh(x)

Parameters

Returns

The acosh() method returns the inverse hyperbolic cosine or cosh⁻¹ of x in radians. The result is between the range 0 and ∞, including 0.

Example Codes: Use Python math.acosh() to Compute Inverse Hyperbolic Cosine of a Value

import math

print(f"cosh⁻¹({1}) : {math.acosh(1)} radians")
print(f"cosh⁻¹({10}) : {math.acosh(10)} radians")
print(f"cosh⁻¹({200}) : {math.acosh(200)} radians")
print(f"cosh⁻¹({5000}) : {math.acosh(5000)} radians")
print(f"cosh⁻¹({99999}) : {math.acosh(99999)} radians")

Output:

cosh⁻¹(1) : 0.0 radians
cosh⁻¹(10) : 2.993222846126381 radians
cosh⁻¹(200) : 5.9914582970493875 radians
cosh⁻¹(5000) : 9.210340361976183 radians
cosh⁻¹(99999) : 12.206062645455173 radians

The Python code above computes the inverse of cosine or arccosine for 1, 10, 200, 5000, and 99999. Note that all the results are in the range [0, ∞).

Example Codes: Use Python math.acosh() to Compute Arccosine and Cosine

import math

inputs = [1, 10, 200, 5000, 99999]

for x in inputs:
    acosh = math.acosh(x)
    print(f"cosh⁻¹({x}):", acosh)
    print(f"cosh({acosh}):", math.cosh(acosh))

Output:

cosh⁻¹(1): 0.0
cosh(0.0): 1.0
cosh⁻¹(10): 2.993222846126381
cosh(2.993222846126381): 9.999999999999998
cosh⁻¹(200): 5.9914582970493875
cosh(5.9914582970493875): 200.0
cosh⁻¹(5000): 9.210340361976183
cosh(9.210340361976183): 5000.000000000001
cosh⁻¹(99999): 12.206062645455173
cosh(12.206062645455173): 99999.00000000001

The Python code above calculates inverse hyperbolic cosine of some value x and uses its result to re-compute x using hyperbolic cosine. It performs the above operation for 1, 10, 200, 5000, and 99999.