inverse cotangent
Học thuậtThân thiện
Definition
- Noun:
- The inverse function of the cotangent: The
inverse cotangentis 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 cotangentof 1. - The value of the
inverse cotangentof √3 is π/6 radians. - In solving the triangle, we applied the
inverse cotangentfunction.
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
- the inverse function of the cotangent; the angle that has a cotangent equal to a given number