arctangent

Thân thiện

The student calculates the arctangent of the ratio on the whiteboard.

Definition

1. Noun:
   • The inverse function of the tangent: The arctangent is 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 arctangent of 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 arctangent function is called atan.

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, atan2 is preferred over the basic arctangent.

Variants and Related Words

• Arctan (n): A common abbreviation for .
  • The symbol for arctan is 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 arctangent is important.

Học thuật

Noun

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

Từ đồng nghĩa

• arc tangent
• arctan
• inverse tangent