inverse cotangent

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inverse cotangent

The student calculates the inverse cotangent of the ratio on the worksheet.

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 .
inverse cotangent

The student calculates the inverse cotangent of the ratio on the worksheet.

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

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