arccotangent
Definition
- Noun:
- The inverse function of the cotangent: The
arccotangentof a number is the angle (usually measured in radians or degrees) whose cotangent is that given number. It is the principal value of the inverse of the cotangent function.
Usage
- The function, often written as or , returns an angle. Its output range is typically defined as (0, π) radians or (0°, 180°) to provide a single, principal value for each input.
- It is used to find an angle when the value of the cotangent (the ratio of the adjacent side to the opposite side in a right triangle) is known.
Examples
- Noun:
- If cot(θ) = 1, then θ = arccot(1) = π/4 radians (or 45°).
- The value of
arccotangent(√3)is π/6 radians. - To solve for the angle, you must apply the
arccotangentto both sides of the equation.
Advanced Usage
- Domain and Range: The function is defined for all real numbers. Its principal value range is 0 < y < π, which differs from the function's range of -π/2 < y < π/2.
- Relationship with Arctangent: For real , is often computed as for x > 0, with an adjustment for x < 0 to maintain the principal value range.
- In Mathematical Notation: The equation means that and is in the interval (0, π).
Variants and Related Words
- Arccot (n): A common abbreviated form of .
- Calculate arccot(2).
- Inverse Cotangent (n): A synonymous phrase for .
- Arc Function (n): A general term for inverse trigonometric functions like , , and .
Synonyms
- Inverse Cotangent: The direct descriptive synonym.
- Cot⁻¹: The standard mathematical notation synonym.
Related Phrases and Concepts
- Principal Value: The returns the principal value of the angle.
- Trigonometric Identity: for x > 0. For x < 0, to keep the result in (0, π).
Noun
-
the inverse function of the cotangent; the angle that has a cotangent equal to a given number
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