1. What is Inverse Cotangent?

The inverse cotangent function, denoted as arccot(x) or cot⁻¹(x), is the inverse function of the cotangent. It returns the angle whose cotangent is the given number x.

2. How Does the Calculator Work?

The calculator uses the mathematical identity:

Where:

• \( x \) — Input value (dimensionless)
• \( \arctan \) — Inverse tangent function

Explanation: The calculator computes the inverse tangent of the reciprocal of the input value to obtain the inverse cotangent.

3. Mathematical Definition

Details: The inverse cotangent function is defined for all real numbers except zero. It returns values in the range (0, π) radians or (0°, 180°).

4. Using the Calculator

Tips: Enter any real number except zero. The calculator will return the result in both radians and degrees. Ensure the input is a valid number.

5. Frequently Asked Questions (FAQ)

Q1: Why can't x be zero?
A: Division by zero is undefined in mathematics, so the inverse cotangent of zero is not defined.

Q2: What is the range of arccot(x)?
A: The principal value range is (0, π) radians or (0°, 180°).

Q3: How is arccot(x) related to arctan(x)?
A: arccot(x) = arctan(1/x) for x > 0, and arccot(x) = π + arctan(1/x) for x < 0.

Q4: Can I use this for complex numbers?
A: This calculator is designed for real numbers only. Complex number calculations require specialized mathematical software.

Q5: What are practical applications of inverse cotangent?
A: Inverse cotangent is used in trigonometry, calculus, engineering calculations, and signal processing applications.