arctangent
Definition
- Noun:
- The inverse function of the tangent: The
arctangentis a mathematical function that, for a given number (representing the tangent of an angle), returns the corresponding angle. It is the principal inverse of the tangent function. - The angle whose tangent is a given number: The
arctangentof a number is the angle (typically measured in radians or degrees) whose tangent value equals that number.
Usage Examples
- Noun:
- To find the angle in a right triangle when you know the ratio of the opposite side to the adjacent side, you use the
arctangent. - The value of
arctangent(1) is π/4 radians, or 45 degrees. - In many programming languages, the
arctangentfunction is calledatan.
Advanced Usage
- Two-argument arctangent (
atan2): In advanced mathematics and computing, a related function is often used. It computes the of the quotient y/x, but uses the signs of both arguments to determine the correct quadrant of the resulting angle, providing a full 360-degree range.- For precise angular calculations in navigation,
atan2is preferred over the basicarctangent.
Variants and Related Words
- Arctan (n): A common abbreviation for .
- The symbol for
arctanis tan⁻¹.
- Inverse tangent (n): A synonym for .
- The inverse tangent function is essential for solving trigonometric equations.
Synonyms
- Inverse tangent: The direct synonym, describing the same mathematical operation.
- tan⁻¹: The standard mathematical notation for the function.
Related Phrases & Contexts
- Principal value: The function typically returns the principal value, which is the angle in the range (-π/2, π/2) for real inputs.
- The calculator gives the principal value when you compute an
arctangent.
- Branch of the arctangent: In complex analysis, the is a multi-valued function, and one must specify which branch is being used.
- When working with complex numbers, the choice of branch for the
arctangentis important.
Noun
-
the inverse function of the tangent; the angle that has a tangent equal to a given number
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