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

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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.   Please post comments if you find anything wrong or if you would like to share more information on the topic discussed above.

```

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