arc cotangent

Thân thiện

A student calculates the arc cotangent of a value on a scientific calculator.

Definition

1. Noun:
   • The inverse function of the cotangent: The arc cotangent is 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 cotangent of 1, which is π/4 radians.
  • The value of arccot(√3) is π/6.
  • In solving the triangle, we used the arc cotangent function 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.

Học thuật

Noun

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

Từ đồng nghĩa

• arccotangent
• inverse cotangent