Definition

1. Noun:
   • The inverse function of the cotangent: The inverse cotangent is a mathematical function that, for a given number, returns the angle whose cotangent is that number. It is the function that reverses, or "undoes," the action of the cotangent function.

Usage

• The is used to find an angle when the value of the cotangent is known.
• It is typically denoted as , , or .
• Its output is an angle, usually measured in radians or degrees.

Examples

• Noun:
  • To find the angle θ, you need to calculate the inverse cotangent of 1.
  • The value of the inverse cotangent of √3 is π/6 radians.
  • In solving the triangle, we applied the inverse cotangent function.

Advanced Usage

• Principal Value: The function is typically defined to return values in a specific range (e.g., (0, π) for ) to make it a proper function. This is known as its principal value branch.
• Relation to Inverse Tangent: The can be expressed in terms of the inverse tangent: for .

Variants and Related Words

• arccotangent (n): Another name for the inverse cotangent function.
• arc cot (n): A common abbreviated written form.
• Inverse trigonometric function (n): The general category of functions that includes , inverse sine, inverse cosine, etc.

Synonyms

• arccotangent: The direct synonym.
• arc cot: A shortened form.

Related Mathematical Concepts

• Domain and Range: The domain of the is all real numbers. The range (principal value) is typically (0, π).
• Derivative: The derivative of is .

Noun

1. the inverse function of the cotangent; the angle that has a cotangent equal to a given number