Refresher and Functions

Python operators

The following operators can be used to perform basic mathematical calculations in Python

Name	Operator
Addition	+
Subtraction	-
Multiplication	*
Division	/
Modulus	&
Exponentiation	**

Essential mathematical functions

Here is a list of the most useful functions available in Python for maths.

To use these make sure you imported the Numpy module:

import numpy as np

Trigonometric functions

• np.sin(x) calculates the sin of x (in radians)
• np.cos(x) calculates the cosine of x (in radians)
• np.tan(x) calculates the tangent of x (in radians)
• np.arcsin(x) calculates the inverse sin of x (in radians)
• np.arccos(x) calculates the inverse cosine of x (in radians)
• np.arctan(x) calculates the inverse tangent of x (in radians)
• np.degrees(x) angles from radians to degrees
• np.radians(x) angles from degrees to radians

Hyperbolic functions

• np.sinh(x) calculates the hyperbolic sin of x (in radians)
• np.cosh(x) calculates the hyperbolic cosine of x (in radians)
• np.tanh(x) calculates the hyperbolic tangent of x (in radians)
• np.arcsinh(x) calculates the inverse hyperbolic sin of x (in radians)
• np.arccosh(x) calculates the inverse hyperbolic cosine of x (in radians)
• np.arctanh(x) calculates the inverse hyperbolic tangent of x (in radians)

Exponents and logarithms

• np.exp(x) calculate the exponential of all elements in the input x
• np.sqrt(x) calculate square root of x
• np.log(x) calculate the natural logarithm of x
• np.log10(x) calculate the base 10 logarithm of x

Drawing functions

You can easily draw functions using the matplotlib module.

So make sure you import the module:

import matplotlib.pyplot as plt  

Here are some essential functions needed to plot a graph:

• plt.title(x) input string to be graph title
• plt.plot(x, y) plot x and y coordinates, inputs must be arrays
• plt.show() show the graph

For example, to plot the function sin(x)^2 with x between -4 and 4, you could write the following code:

import numpy as np 
import matplotlib.pyplot as plt  

# Compute the x and y coordinates for points on curve 
x = np.arange(-4, 4, 0.1) # Generate array of numbers between -4 and 4 with step size of 0.1 for x coordinates
y = np.sin(x)**2
plt.title("sine wave form") 

# Plot the points using matplotlib 
plt.plot(x, y) 
plt.show() 

Try it out