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# How to use inverse hyperbolic functions in Ruby

harris910

### The asinh() function

The asinh() function returns the inverse hyperbolic sine of a number.

The figure below shows the mathematical representation of the asinh() function:

$asinh(x) =ln(x+√(x^{2}+1))$

### The acosh() function

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

The figure below shows the mathematical representation of the acosh() function:

$acosh(x) =ln(x+√(x^{2}-1))$

### The atanh() function

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

The figure below shows the mathematical representation of the atanh() function:

$atanh(x)=\frac {1}{2}ln(\frac {1+x}{1-x})$

### Syntax

asinh(angle)
acosh(angle)
atanh(angle)


### Parameters

These functions require an angle in radians as a parameter.

• The angle sent to acosh() should be greater than 1 otherwise it returns domain error.
• The angle sent to atanh() should be between 1 and -1 otherwise it returns domain error.

### Return value

• The asinh() function returns the inverse hyperbolic sine of the angle sent as a parameter.

• The acosh() function returns the inverse hyperbolic cosine of the angle sent as a parameter.

• The atanh() function returns the inverse hyperbolic tangent of the angle sent as a parameter.

### Example

The code below demonstrates how to use the inverse hyperbolic functions function in Ruby:

#positive number in radians
print "The value of asinh(0.5) : ",  Math.asinh(0.5), "\n"
print "The value of acosh(1.5) : ",  Math.acosh(1.5), "\n"
print "The value of atanh(0.5) : ",  Math.atanh(0.5), "\n"

print "The value of asinh(-0.5) : ",  Math.asinh(-0.5), "\n"
print "The value of atanh(-0.5) : ",  Math.atanh(-0.5), "\n"

#zero
print "The value of asinh(0) : ",  Math.asinh(0), "\n"
print "The value of atanh(0) : ",  Math.atanh(0), "\n"


### Explanation

• Lines 2–4 : We calculate the inverse hyperbolic function of the positive number in radians.
• Lines 7–8 : We calculate the inverse hyperbolic function of the negative number in radians.
• Lines 11–12 : We calculate the inverse hyperbolic function of the zero in radians.

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