## Exploration of NumPy Trigonometric Function Series

NumPy, or Numerical Python, is a fundamental library in the Python language that allows the performance of large and complex numerical computations in a fast and efficient manner. One of its core functionality is the implementation of a series of trigonometric functions, which includes the cosine function or Cos.

NumPy Trigonometric Function series includes sine, cosine, tangent, hyperbolic sine, cosine, and tangent. These functions are commonly used in mathematics, physics, engineering, and other scientific fields to solve complex problems related to angles, curves, and waves.

## Definition and Output Range of NumPy Cos Function

NumPy Cos function, as the name suggests, computes the cosine of an input angle value. It returns the cosine of the input angle in radians.

Its definition is as follows:

`numpy.cos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) -> ndarray`

The output range of the NumPy Cos function is between -1 and 1. It implies that the cosine value of an angle can only range from -1 to 1, with -1 being the horizontal and 1 being vertical.

## Purpose of the Tutorial

The main objective of this tutorial is to provide an overview of the NumPy Cos function, its syntax, and examples to enable readers to understand how to utilize the function in their numerical computations.

## Syntax and Examples of NumPy Cos Function

### Syntax of NumPy Cos Function

The syntax of the NumPy Cos function is as follows:

`numpy.cos(x)`

Here, x is the input argument in radians, and the function returns an ndarray value of cosine of x.

### Example of Cosine Values for Pi Values

To calculate the cosine values for pi values, you can use the following code:

```
import numpy as np
pi = np.pi
print("Cosine of 0 is: ", np.cos(0))
print("Cosine of pi/4 is: ", np.cos(pi/4))
print("Cosine of pi/2 is: ", np.cos(pi/2))
print("Cosine of pi is: ", np.cos(pi))
```

#### You will get the following output:

```
Cosine of 0 is: 1.0
Cosine of pi/4 is: 0.7071067811865476
Cosine of pi/2 is: 6.123233995736766e-17
Cosine of pi is: -1.0
```

#### Explanation of Why Cosine of pi/2 Produces a Different Output

The output of the cosine of pi/2 produces a small positive value instead of 0. The reason for this is that numpy stores floating-point numbers as a finite number of binary digits, which may result in tiny errors that accumulate over calculations.

Hence, when the cosine of pi/2 is calculated, this error propagates, and the result is a small positive number instead of zero.

### Example of Passing Degrees as an Argument Using deg2rad Function

To convert the degree to radian and then find the cosine value, you can use the deg2rad function as follows:

```
import numpy as np
angle_in_degree = 45
angle_in_radian = np.deg2rad(angle_in_degree)
cos_val = np.cos(angle_in_radian)
print("Cosine of ", angle_in_degree, " degrees is: ", cos_val)
```

#### You will get the following output:

`Cosine of 45 degrees is: 0.7071067811865476`

### Example of Cosine Values for an Array of Angles

To calculate the cosine values for an array of angles, you can pass an array of angles as input to the NumPy Cos function as follows:

```
import numpy as np
angles = np.array([0, 30, 45, 60, 90])
cos_val_array = np.cos(np.deg2rad(angles))
print("Cosine values of angles: ", angles, " are: ", cos_val_array)
```

#### You will get the following output:

```
Cosine values of angles: [ 0 30 45 60 90] are: [1. 0.8660254 0.70710678 0.5 0.
]
```

### Example of Using numpy.linspace to Create Equally Spaced Angles

numpy.linspace function is used to create an array of evenly-spaced numbers over a specified interval. To create an array of evenly spaced angles, use the following code:

```
import numpy as np
angles = np.linspace(0,90,9)
cos_val_array = np.cos(np.deg2rad(angles))
print("Cosine values of angles: ", angles, " are: ", cos_val_array)
```

#### You will get the following output:

```
Cosine values of angles: [ 0. 10.
20. 30.
40. 50.
60. 70.
80. 90.] are: [1.
0.98480775 0.93969262 0.8660254 0.76604444 0.64278761 0.5
0.34202014 0.17364818 0. ]
```

## Visualization of Cosine Function Using Matplotlib

### Import of Matplotlib library

Matplotlib is a powerful data visualization library that can be used to create graphs, plots, and charts. Before starting with the visualization of the cosine function, let’s import the Matplotlib library using the following code:

`import matplotlib.pyplot as plt`

With this code, we can import the library and use the abbreviation plt to reference it in subsequent code.

### Example of Creating a NumPy Array of Evenly Spaced Angles

To create an array of evenly spaced angles, NumPy’s linspace function can be used. The linspace function creates an array of equally spaced values within a specified range.

To create an array of angles between 0 and 2, the function can be called using the following code:

```
import numpy as np
angles = np.linspace(0, 2*np.pi, 100)
```

In this code, the linspace function creates an array of 100 evenly spaced angles between 0 and 2 (two times the mathematical constant pi, which expresses the ratio of a circle’s circumference to its diameter, rounded to 3.14).

### Example of Plotting the Cosine Function Using plt.plot()

Finally, we can use the plt.plot() function to plot the cosine function using the array of angles created above.

We can use the following code to plot the cosine function:

```
import numpy as np
import matplotlib.pyplot as plt
angles = np.linspace(0, 2*np.pi, 100)
cos_vals = np.cos(angles)
plt.plot(angles, cos_vals)
plt.xlabel('Angle (radians)')
plt.ylabel('Cosine')
plt.title('Plot of Cosine Function')
plt.show()
```

This code will create a plot of the cosine function for angles that range from 0 to 2. The resulting plot displays a bell-shaped curve with a maximum value of 1, a minimum value of -1, and zeros at equal intervals in the range.

Axes get labeled with ‘Angle (radians)’ and ‘Cosine’. The title of the graph is ‘Plot of Cosine Function’.

## Conclusion

In conclusion, the NumPy Cos function is an important tool for performing complex numerical calculations related to angles and waves. It has a simple syntax and can be easily incorporated into your Python code.

This tutorial provided an overview of the definition, output range, syntax, and examples of using the NumPy Cos function. With the knowledge gained through this tutorial, you can effectively utilize this function in your scientific and engineering computations. The NumPy Cos function provides a quick and efficient way to calculate the cosine of an angle in Python.

This tutorial touched on just a few examples of how it can be used in practical computing applications. However, there are a multitude of applications that can make use of the cosine function and Python programming.

By practicing with more examples, you will gain exposure to a broader range of tasks you can perform using the NumPy Cos function and other related tools. In summary, this tutorial provided an overview of the NumPy Cos function, a core functionality of the NumPy library, used in numerical computations in science, engineering, and mathematics.

The article covered the definition, output range, syntax, and examples of the NumPy Cos function. Additionally, the article demonstrated how to visualize the cosine function using the Matplotlib library and create evenly spaced angles.

An important takeaway here is that NumPy Cos function offers a straightforward way to compute the cosine of an angle in Python. This tutorial encourages the reader to practice more examples and explore other related tools in NumPy library to improve their numerical computation skills.