1. What is Inverse Cotangent?

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

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 find the inverse cotangent.

3. Applications of Inverse Cotangent

Details: The inverse cotangent function is used in various fields including trigonometry, calculus, engineering, and physics for solving equations involving cotangent relationships.

4. Using the Calculator

Tips: Enter any real number (except 0) to calculate its inverse cotangent. The result is provided in both radians and degrees for convenience.

5. Frequently Asked Questions (FAQ)

Q1: Why can't I input zero?
A: The inverse cotangent of zero is undefined because it would require division by zero in the calculation.

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

Q3: How is this different from arctan(x)?
A: While arctan(x) gives the angle whose tangent is x, arccot(x) gives the angle whose cotangent is x. They are related but distinct functions.

Q4: Can I calculate inverse cotangent for negative values?
A: Yes, the calculator accepts negative values and will return the appropriate angle in the correct quadrant.

Q5: What are some practical uses of inverse cotangent?
A: It's used in solving trigonometric equations, signal processing, and in various engineering calculations involving angles and ratios.