arc cotangent
Definition
- Noun:
- The inverse function of the cotangent: The
arc cotangentis a trigonometric function that, for a given number (which is a cotangent value), returns the corresponding angle. It is the inverse operation of taking the cotangent of an angle.
Usage
- The is used in mathematics, particularly in trigonometry, geometry, and calculus, to find an angle when its cotangent value is known.
- It is typically denoted as or .
- The output (the angle) is usually expressed in radians or degrees.
Examples
- Noun:
- To find the angle whose cotangent is 1, you calculate the
arc cotangentof 1, which is π/4 radians. - The value of
arccot(√3)is π/6. - In solving the triangle, we used the
arc cotangentfunction to determine the unknown angle.
Advanced Usage
- Principal Value: The function is typically defined to return an angle in the range (0, π) for real inputs, which is its principal value branch.
- Relation to Arc Tangent: For real , is often defined as .
- Calculus: The derivative of is .
Variants and Related Words
- arccot: A common abbreviated notation for .
- The solution is written as θ = arccot(2).
- Inverse Cotangent: A fully synonymous term.
- The inverse cotangent function is used in the formula.
- Cot⁻¹: An alternative symbolic notation using the superscript "-1".
- The angle α can be expressed as α = cot⁻¹(y/x).
Synonyms
- Inverse Cotangent: The direct synonym, describing the same mathematical function.
Related Phrases
- Arc Functions: A category of inverse trigonometric functions including , , and .
- Inverse Trigonometric Function: The general class of functions to which belongs.
Noun
-
the inverse function of the cotangent; the angle that has a cotangent equal to a given number
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