Inverse cotangent calculator

Calculate the angle whose cotangent is a given number. The inverse cotangent function, denoted as arccot(x) or cot-1(x), returns the angle θ such that cot(θ) = x.

Input Parameters

Enter a real number. Negative values will return angles in the second quadrant (π to 2π).

Calculation Results

Calculation Formula

arccot(x) = arctan(1/x) = π - arctan(x)

Where:
- arccot(x) is the inverse cotangent of x
- arctan(x) is the inverse tangent of x
- π is the mathematical constant (approximately 3.14159)

Result

Angle in Degrees: --

Angle in Radians: --

Angle in Grads: --

Inverse cotangent calculator Calculator Usage Guide

Learn how to use the Inverse cotangent calculator and its working principles

How to use the calculator

  1. Enter a cotangent value in the input field. This can be any real number except 0.
  2. Click the "Calculate" button to compute the angle.
  3. The result will be displayed in degrees, radians, and gradians.

Understanding the results

The inverse cotangent function returns an angle. The range of arccot(x) is typically (0, π) radians, or (0°, 180°) degrees. If you enter a negative cotangent value, the calculator will return an angle in the second quadrant (between π and 2π).

Mathematical background

The inverse cotangent is related to the inverse tangent function by the formula:

arccot(x) = arctan(1/x) = π - arctan(x)

This relationship helps explain why the range of arccot(x) is different from arctan(x).

Practical applications

The inverse cotangent function is used in various fields including:

  • Trigonometry and geometry calculations
  • Engineering problems involving angles of inclination
  • Computer graphics and image processing
  • Physics calculations involving wave patterns