arc cosecant

Thân thiện

The student calculates the arc cosecant of a value on her calculator.

Definition

1. Noun:
   • The inverse function of the cosecant: The arc cosecant of a number is the angle (usually measured in radians or degrees) whose cosecant equals that given number. It is the principal value of the inverse cosecant function.

Usage

• The is used in trigonometry and calculus to find an angle when the value of the cosecant is known.
• It is typically denoted as arccsc(x), csc⁻¹(x), or arc cosec(x).
• The domain of the function is (-∞, -1] ∪ [1, ∞), and its principal value range is usually [-π/2, 0) ∪ (0, π/2] (in radians).

Examples

Advanced Usage

• Mathematical Context: The is one of the six principal inverse trigonometric functions. Its derivative is d/dx[arccsc(x)] = -1 / (|x|√(x² - 1)) for |x| > 1.
• Principal Value: It is important to specify the range (or branch) when discussing the , as it is a multivalued function. The principal value is the most commonly used output.

Variants and Related Words

• arccsc: The standard abbreviation for .
• inverse cosecant: A synonymous term for .
• arcsecant (arcsec): The inverse of the secant function, related conceptually.
• arcsine (arcsin): The inverse of the sine function, another inverse trigonometric function.

Synonyms

• Inverse cosecant: The direct synonym.
• arccsc: The standard mathematical abbreviation.

Related Phrases and Concepts

• Inverse trigonometric function: The broader category to which belongs.
• Cosecant (csc): The trigonometric function whose inverse is the .

Học thuật

Noun

1. the angle that has a cosecant equal to a given number

Từ đồng nghĩa

• arccosecant
• inverse cosecant