Complex Numbers in Python | Set 3 (trigonometric and hyperbolic functions)

Complex Numbers in Python | Set 2 (Important Functions and Constants)

Trigonometric and hyperbolic functions are discussed in this article.

Trigonometric functions

1. sin () : This function returns the sine of the complex number passed in the argument.

2. cos () : This function returns the cosine of the complex number passed in the argument.

3. tan () : This function returns the tangent of the complex number passed in the argument.

# Python code for demonstration work
# sin (), cos (), tan ()

 
# import & quot; cmath & quot; for operations with complex numbers

import cmath

 
# Initializing real numbers

x = 1.0

 

y = 1.0

 
# convert x and y to complex z

z = complex (x, y); 

 
# printing the sine of a complex number

print ( "The sine value of complex number is:" , end = "")

print (cmath.sin (z))

 
# printing the cosine of a complex number

print ( "The cosine value of complex number is:" , end = "")

print (cmath .cos (z))

 
# complex number print tangent

print ( "The tangent value of complex number is: " , end = " ")

print (cmath.tan (z))

Output:

 The sine value of complex number is: (1.2984575814159773 + 0.6349639147847361j) The cosine value of complex number is: (0.8337300251311491-0.9888977057628651j) The tangent value of complex number is: (0.2717525853195118 + 1.0839233273386946j) 

4. asin () : This function returns the arcsine of the complex number passed in the argument.

5. acos () : This function returns the inverse cosine of the complex number passed in the argument.

6. atan () : This function returns the arctangent of the complex number passed in the argument.

# Python code for demonstration work
# asin (), acos (), atan ()

 
# import & quot; cmath & quot; for operations with complex numbers

import cmath

 
# Initializing real numbers

x = 1.0

 

y = 1.0

 
# convert x and y to complex z

z = complex (x, y); 

 
# printing the sine arc of a complex number

print ( "The arc sine value of complex number is:" , end = "")

print (cmath.asin (z))

 
# printing the arccosine of a complex number

print ( " The arc cosine value of complex number is: " , end = " ")

print (cmath.acos (z))

 
# print arctangent comp lex number

print ( "The arc tangent value of complex number is: " , end = " ")

print (cmath.atan (z))

Output:

 The arc sine value of complex number is: (0.6662394324925153 + 1.0612750619050357 j) The arc cosine value of complex number is: (0.9045568943023814-1.0612750619050357j) The arc tangent value of complex number is: (1.0172219678978514 + 0.40235947810852507j) 

Hyperbolic functions

1. sinh () : This function returns the hyperbolic sine of the complex number passed in the argument.

2. cosh () : This function returns the hyperbolic cosine of the complex number passed in the argument.

3. tanh () : This function returns the hyperbolic tangent of the complex number passed in the argument.

# Python code for demonstrations
# sinh (), cosh (), tanh ()

 
# import & quot; cmath & quot; for operations with complex numbers

import cmath

 
# Initializing real numbers

x = 1.0

 

y = 1.0

 
# convert x and y to complex z

z = complex (x, y); 

 
# printing the hyperbolic sine of a complex number

print ( "The hyperbolic sine value of complex number is:" , end = "")

print (cmath.sinh (z))

 
# printing the hyperbolic cosine of a complex number

print ( "The hyperbolic cosine value of complex number is:" , end = "")

print (cmath.cosh (z))

  
# printing the hyperbolic tangent of a complex number

print ( "The hyperbolic tangent value of complex number is:" , end = "")

print (cmath.tanh (z))

Output:

 The hyperbolic sine value of complex number is: (0.6349639147847361 + 1.2984575814159773j) The hyperbolic cosine value of complex number is: (0.8337300251311491 + 0.9888977057628651j) The hyperbolic tangent value of complex number is: (1.0839233273386946 + 0.2711725853195 p>  4. asinh () : This function returns the  inverse hyperbolic sine  of the complex number passed in the argument. 

5. acosh () : This function returns the inverse hyperbolic cosine of the complex number passed in the argument.

6. atanh () : This function returns the inverse hyperbolic tangent of the complex number passed in the argument.

# Python code to demonstrate how it works
# asinh (), acosh (), atanh ()

  
# import & quot; cmath & quot; for operations with complex numbers

import cmath

 
# Initializing real numbers

x = 1.0

 

y = 1.0

 
# convert x and y to complex z

z = complex (x, y); 

 
# print the inverse hyperbolic sine of a complex number

print ( "The inverse hyperbolic sine value of complex number is:" , end = "")

print (cmath.asinh (z))

 
# print the inverse hyperbolic cosine of a complex number

print ( "The inverse hyperbolic cosine value of complex number is:" , end = "")

print (cmath.acosh (z))

  
# print the inverse hyperbolic tangent of a complex number

print ( "The inverse hyperbolic tangent value of complex number is:" , end = "")

print (cmath.atanh (z))

Output:

 The inverse hyperbolic sine value of complex number is: (1.0612750619050357 + 0.6662394324925153j) The inverse hyperbolic cosine value of complex number is: (1.0612750619050357 + 0.9045568943023813j) The inverse hyperbolic tangolic of complex number is: (0.40235947810852507 + 1.0172219678978514j) 

This article courtesy of Manjit Singh . If you are as Python.Engineering and would like to contribute, you can also write an article using contribute.python.engineering or by posting an article contribute @ python.engineering. See my article appearing on the Python.Engineering homepage and help other geeks.

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