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Complex Numbers in Python | Set 3 (Trigonometric and Hyperbolic Functions)
• Difficulty Level : Easy
• Last Updated : 04 Feb, 2020

Some of the Important Complex number functions are discussed in the articles below

Trigonometric and Hyperbolic Functions are discussed in this article.

Trigonometric Functions

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

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

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

 `# Python code to demonstrate the working of ``# sin(), cos(), tan()``  ` `# importing "cmath" for complex number operations``import` `cmath``  ` `# Initializing real numbers``x ``=` `1.0``  ` `y ``=` `1.0`` ` `# converting x and y into complex number z``z ``=` `complex``(x,y);`` ` `# printing sine of the complex number``print` `(``"The sine value of complex number is : "``,end``=``"")``print` `(cmath.sin(z))`` ` `# printing cosine of the complex number``print` `(``"The cosine value of complex number is : "``,end``=``"")``print` `(cmath.cos(z))`` ` `# printing tangent of the complex number``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 arc sine of the complex number passed in argument.

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

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

 `# Python code to demonstrate the working of ``# asin(), acos(), atan()``  ` `# importing "cmath" for complex number operations``import` `cmath``  ` `# Initializing real numbers``x ``=` `1.0``  ` `y ``=` `1.0`` ` `# converting x and y into complex number z``z ``=` `complex``(x,y);`` ` `# printing arc sine of the complex number``print` `(``"The arc sine value of complex number is : "``,end``=``"")``print` `(cmath.asin(z))`` ` `# printing arc cosine of the complex number``print` `(``"The arc cosine value of complex number is : "``,end``=``"")``print` `(cmath.acos(z))`` ` `# printing arc tangent of the complex 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+1.0612750619050357j)
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 argument.

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

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

 `# Python code to demonstrate the working of ``# sinh(), cosh(), tanh()``  ` `# importing "cmath" for complex number operations``import` `cmath``  ` `# Initializing real numbers``x ``=` `1.0``  ` `y ``=` `1.0`` ` `# converting x and y into complex number z``z ``=` `complex``(x,y);`` ` `# printing hyperbolic sine of the complex number``print` `(``"The hyperbolic sine value of complex number is : "``,end``=``"")``print` `(cmath.sinh(z))`` ` `# printing hyperbolic cosine of the complex number``print` `(``"The hyperbolic cosine value of complex number is : "``,end``=``"")``print` `(cmath.cosh(z))`` ` `# printing hyperbolic tangent of the 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+0.2717525853195117j)
```

4. asinh() : This function returns the inverse hyperbolic sine of the complex number passed in argument.

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

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

 `# Python code to demonstrate the working of ``# asinh(), acosh(), atanh()``  ` `# importing "cmath" for complex number operations``import` `cmath``  ` `# Initializing real numbers``x ``=` `1.0``  ` `y ``=` `1.0`` ` `# converting x and y into complex number z``z ``=` `complex``(x,y);`` ` `# printing inverse hyperbolic sine of the complex number``print` `(``"The inverse hyperbolic sine value of complex number is : "``,end``=``"")``print` `(cmath.asinh(z))`` ` `# printing inverse hyperbolic cosine of the complex number``print` `(``"The inverse hyperbolic cosine value of complex number is : "``,end``=``"")``print` `(cmath.acosh(z))`` ` `# printing inverse hyperbolic tangent of the 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 tangent value of complex number is : (0.40235947810852507+1.0172219678978514j)
```

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