arccotangent

Thân thiện

The student calculates the arccotangent of the value on the calculator.

Definition

1. Noun:
   • The inverse function of the cotangent: The arccotangent of 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 arccotangent to 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).

Học thuật

Noun

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

Từ đồng nghĩa

• arc cotangent
• inverse cotangent