Inverse Cotangent Calculator

Category: Algebra II
- November 19, 2025
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Calculate the inverse cotangent (arccot) of a value, which gives you the angle whose cotangent equals the input value. The range of inverse cotangent is (0, π) radians or (0°, 180°).

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Note: Inverse cotangent is defined for all real numbers

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About Inverse Cotangent

The inverse cotangent, also called arccot or cot-1, is the inverse function of the cotangent. It returns the angle whose cotangent equals the given value.

Properties of Inverse Cotangent
  • Domain: All real numbers (ℝ)
  • Range: (0, π) radians or (0°, 180°)
  • Not Periodic: Unlike cotangent, the inverse cotangent is not a periodic function
  • Decreasing Function: arccot(x) decreases as x increases
Relationships with Other Inverse Trigonometric Functions
  • arccot(x) = arctan(1/x)
  • arccot(x) = π/2 - arctan(x) for x > 0
  • arccot(x) = -π/2 - arctan(x) for x < 0
  • arccot(-x) = π - arccot(x)
Special Values
  • arccot(0) = π/2 ≈ 1.57 rad (90°)
  • arccot(1) = π/4 ≈ 0.79 rad (45°)
  • arccot(√3) = π/6 ≈ 0.52 rad (30°)
  • arccot(∞) approaches 0
  • arccot(-∞) approaches π
Applications

Inverse cotangent is used in various fields including:

  • Engineering and physics (signal processing, control theory)
  • Complex analysis and electrical engineering
  • Navigation and surveying
  • Computer graphics (rotations and transformations)

What is the Inverse Cotangent Calculator?

The Inverse Cotangent Calculator is a helpful tool for finding the angle whose cotangent equals a specific value. This calculation, known as arccot, can be valuable in various fields. The calculator can display results in both degrees and radians, making it versatile for different user needs.

How to Use the Inverse Cotangent Calculator

Using the calculator is straightforward. You enter a cotangent value, choose the angle unit, and select how many decimal places you want in the result. After that, the calculator does the work for you, showing the angle in degrees and radians, along with some Other useful information.

Understanding the Results

When you input a value, the calculator presents the inverse cotangent in degrees and radians. It also provides related angles and a visualisation of the unit circle. This helps users grasp the concept better and see where the angle lies within the circle.

Key Features of the Inverse Cotangent Calculator

  • Calculates arccot(x) efficiently.
  • Displays results in degrees or radians based on your selection.
  • Offers options for showing calculation steps and related angles.
  • Visualises results using a unit circle for a better understanding.

Properties of the Inverse cotangent function

The inverse cotangent function has some interesting properties. Its domain includes all real numbers, which means you can input any real number. The range of the function is from 0 to π radians (or 0° to 180°). Importantly, it’s a decreasing function, which means as the input value increases, the output angle decreases.

Relationships with Other trigonometric functions

The inverse cotangent function relates to other trigonometric functions in various ways. Here are some important relationships:

  • arccot(x) = arctan(1/x)
  • arccot(x) = π/2 - arctan(x) for x > 0
  • arccot(x) = -π/2 - arctan(x) for x < 0
  • arccot(-x) = π - arccot(x)

Special Values to Remember

Some special values of the inverse cotangent function are easy to remember and can be handy for quick calculations. For instance:

  • arccot(0) = π/2 (or 90°)
  • arccot(1) = π/4 (or 45°)
  • arccot(√3) = π/6 (or 30°)
  • arccot(∞) approaches 0
  • arccot(-∞) approaches π

Applications of the Inverse Cotangent Function

The inverse cotangent has various applications in real-world scenarios. It’s commonly used in fields like Physics and engineering, particularly in signal processing and control theory. Additionally, it plays a role in computer graphics when handling rotations and transformations, as well as in navigation and surveying tasks.