Complex Numbers in Python | Set 3 (Trigonometric and Hyperbolic Functions)

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

Complex Numbers in Python | Set 1 (Introduction)
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 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)