1. What is Cot Inverse?

The cot inverse 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 x.

2. How Does the Calculator Work?

The calculator uses the mathematical identity:

Where:

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

Explanation: This identity allows us to compute the inverse cotangent using the more commonly available inverse tangent function.

3. Applications of Cot Inverse

Details: The cot inverse function is used in various mathematical and engineering applications, particularly in trigonometry, calculus, and signal processing where angle calculations are required.

4. Using the Calculator

Tips: Enter any real number x (x ≠ 0) in the input field. The calculator will compute both the radian and degree values of arccot(x).

5. Frequently Asked Questions (FAQ)

Q1: Why can't x be zero?
A: Division by zero is undefined in mathematics, so arccot(0) is not defined.

Q2: What is the range of arccot(x)?
A: The principal value of arccot(x) is typically defined on the interval (0, π) radians or (0°, 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 represent different trigonometric relationships.

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

Q5: What's the relationship between cot and tan?
A: Cotangent is the reciprocal of tangent: cot(θ) = 1/tan(θ), which is why arccot(x) = arctan(1/x).