In this tutorial, I’ll show you how to use the Numpy arctan function to compute the trigonometric arctangent in Python.
I’ll explain the syntax of np.arctan, how the function works, and how to use it.
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Table of Contents:
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A Quick Introduction to Numpy Arctan
The Numpy arctan function computes the trigonometric arctangent in Python.
I’ll show you how to do both, but first, we’ll look at the syntax.
The syntax of np.arctan
The syntax for the Numpy arctan function is fairly simple:
This, of course, assumes that you’ve imported Numpy with the alias
np, which is the common convention.
Acceptable formats for the input
Let’s briefly discuss at the acceptable input types for the np.arctan function.
In the image of the syntax shown above, you can see that the input to the function is labeled “
It’s important to mention that this input can take one of several different forms:
- a number (integer or float)
- a Numpy array (of integers or floats)
- a Python list of number, or list-like object
The np.arctan will operate on all of these inputs. Having said that, these different inputs will produce slightly different outputs
The output of np.arctan
The format of the output depends slightly on the input:
- if the input is a single number, then the output will be a single number (the arctangent of the input)
- if the input is a Numpy array, a Python list, or a list-like object, then the output will be a Numpy array of the arctangents
In addition to the input argument, the np.arctan function has some optional parameters:
These are somewhat rarely used, but so I won’t explain them here.
Examples of how to use the Numpy arctangent function
Now that we’ve taken a look at the syntax for the Numpy arctangent function, let’s look at some examples.
- Compute the arctangent of 0
- Compute the arctangent of 1,000,000
- Use the Numpy arctangent function on a Numpy array of values
- Plot the arctangent function (using Plotly)
Preliminary code: Import Numpy and Set Up Plotly
Before you run the examples, you’re going to need to run some preliminary code.
Specifically, you’ll need to import the packages we’re going to use.
You also may need to set up image rendering for Plotly (if you’re using an IDE).
First, you can import Numpy and Plotly with this code.
import numpy as np import plotly.express as px
Obviously, we’ll use Numpy to run the np.arctan function.
But we’ll also use Plotly to plot the arctan function in example 4.
Set Up Image Rendering
Next, if you’re using an IDE like Spyder or PyCharm, you may need to set up your IDE so that it will render output images from Plotly.
By default, Plotly is set up to send output visualizations to your browser. That’s fine if you’re working in a notebook, but if you’re using an IDE, it will just cause an error.
So if you’re using an IDE, you’ll need to tell Plotly to render the output visualizations as svg images.
You can do that with the following code:
(Note: if you’re using Jupyter, you can skip this code!)
import plotly.io as pio pio.renderers.default = 'svg'
Once you’re run the setup code, you should be ready to run the examples.
EXAMPLE 1: Compute the arctangent of 0
Let’s start with a simple example.
Here, we’re going to compute the arctangent of 0.
Obviously, this is very simple.
We’ve used np.arctan to compute the arctangent of 0, which is 0.0.
(Note that np.arctan outputs floating point numbers.)
EXAMPLE 2: Compute the arctangent of 1,000,000
Now we’re going to compute the arctangent of 1,000,000.
Here, we’ve computed the arctan of 1,000,000.
Effectively though, what I’m doing is computing the arctangent of a relatively large number.
The output is 1.5707953267948966.
You might not recognize this, but it’s approximately .
This is important, because as , .
EXAMPLE 3: Use the Numpy arctan function on a Numpy array of values
Next, we’re going to use the Numpy arctan function on a Numpy array.
Create Numpy Array
First, let’s just create a Numpy array.
We’ll use Numpy linspace to create an array that contains 300 evenly spaced numbers from -10 to 10.
x_values = np.linspace(start = -10, stop = 10, num = 300)
Compute Arctangents using Numpy
Next, we’re going to compute the arctangent of every number in our array,
To do that, we provide
x_values as the input to the function:
arctan_values = np.arctan(x_values)
Let’s take a look at the first few values of
arctan_values, so we can see what’s inside:
array([-1.47046099, -1.46978535, -1.46910058, -1.4684065 , -1.46770291, -1.46698962, -1.46626643, -1.46553313, -1.46478951])
This is fairly straightforward.
Here, np.arctan has computed the arctangent of every element in
EXAMPLE 4: Plot the arctangent function using Plotly
Finally, let’s plot the arctangent function.
To do this, we’ll use Plotly to plot the values in
arctan_values, which we computed in example 3.
Specifically, we’ll use the Plotly line function, px.line, to plot the data:
px.line(x = x_values, y = arctan_values)
Here, we’ve plotted the arctangent function with the Plotly line function.
We’ve plotted the values in
x_values on the x-axis.
And we plotted the values in
arctan_values, which we computed with np.arctan, on the y-axis.
Leave your other questions in the comments below
Do you have other questions about how to use np.arctan?
If so, leave your questions in the comments section below.
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