MongoDB $tan Operator

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Introduction

In MongoDB's aggregation framework, the $tan operator serves as a valuable tool for computing the tangent of a given angle. This operator facilitates various trigonometric calculations, enabling users to analyze and manipulate numerical data effectively.

Let's delve into the details of how the $tan operator can be utilized within MongoDB's aggregation pipelines.

Syntax

The syntax for the $tan method is straightforward:

syntax.js

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{ $tan: <angle> }

• $tan: This operator signifies that the subsequent operation will compute the tangent of the specified angle.
• <angle>: This represents the angle (in radians) for which the tangent will be calculated. It could be a field reference, a mathematical expression, or a value.

Example

Input

Consider a collection named angles containing documents with fields degrees representing angles in degrees. Here are sample documents from the angles collection:

Input

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[
  { "_id": ObjectId("609c26812e9274a86871bc6a"), "degrees": 30 },
  { "_id": ObjectId("609c26812e9274a86871bc6b"), "degrees": 45 },
  { "_id": ObjectId("609c26812e9274a86871bc6c"), "degrees": 60 }
]

Aggregation

Suppose we want to compute the tangent of each angle in radians. Here's how you can achieve this using the $tan operator:

example.js

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db.angles.aggregate([
  {
    $project: {
      tangent: { $tan: { $degreesToRadians: "$degrees" } }
    }
  }
])

Explanation

• $degreesToRadians: This operator converts degrees to radians, as the $tan operator expects angles in radians.
• $tan: Computes the tangent of the angle (in radians).

When discussing how the above aggregation works:

1. For the document with "_id" 609c26812e9274a86871bc6a and "degrees" equal to 30:
   • Convert 30 degrees to radians: 30 * (π / 180) ≈ 0.5236 radians
   • Calculate the tangent of 0.5236 radians: tan(0.5236) ≈ 0.5774
2. For the document with "_id" 609c26812e9274a86871bc6b and "degrees" equal to 45:
   • Convert 45 degrees to radians: 45 * (π / 180) ≈ 0.7854 radians
   • Calculate the tangent of 0.7854 radians: tan(0.7854) ≈ 1
3. For the document with "_id" 609c26812e9274a86871bc6c and "degrees" equal to 60:
   • Convert 60 degrees to radians: 60 * (π / 180) ≈ 1.0472 radians
   • Calculate the tangent of 1.0472 radians: tan(1.0472) ≈ 1.7321

Output

Now, let's take a look at the output generated by the aggregation pipeline:

Output

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{ "_id": ObjectId("609c26812e9274a86871bc6a"), "tangent": 0.5774 }
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "tangent": 1 }
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "tangent": 1.7321 }

Use Cases

1. Geometry and Trigonometry:

   The $tan operator is essential for performing trigonometric computations, such as calculating slopes, angles, and distances in geometric applications.

2. Engineering and Physics:

   Tangent values are frequently used in engineering simulations, physics experiments, and mathematical modeling.

3. Data Analysis:

   Trigonometric functions play a significant role in various data analysis tasks, such as signal processing, time-series analysis, and spatial data analysis.

Conclusion

The $tan operator in MongoDB's aggregation framework provides a convenient means of computing tangents within aggregation pipelines, facilitating a wide range of trigonometric calculations. Whether you're working with geometric data, engineering simulations, or mathematical models, mastering the usage of $tan empowers you to analyze and manipulate numerical data effectively within MongoDB.

With its intuitive syntax and versatile applications, the $tan operator proves to be a valuable asset for handling numerical data within MongoDB's aggregation framework. Incorporate it into your aggregation pipelines to unlock new possibilities in data analysis and gain deeper insights into your datasets.

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