arcsec

Thân thiện

The student calculates the arcsec of a value on her calculator.

Definition

Noun: - The inverse function of the secant: In trigonometry, arcsec is the inverse (or arc) function of the secant. For a given number x (where |x| ≥ 1), arcsec(x) returns the angle (typically measured in radians) whose secant is x.

Usage

• is used to find an angle when the value of its secant is known.
• It is commonly written as or .
• The output (the angle) is usually restricted to a specific range, most commonly [0, π] excluding π/2, to ensure it is a proper function.

Examples

Advanced Usage

• Domain and Range: The domain of is (-∞, -1] ∪ [1, ∞). Its principal value range is usually [0, π] except for π/2.
• Relationship with Arccosine: can be expressed in terms of the arccosine function: for x ≥ 1 or x ≤ -1.
• Derivative: In calculus, the derivative of is for |x| > 1.

Variants and Related Words

• Arcsecant: A full, alternative name for the function.
• sec⁻¹: An alternative notation for , where the "-1" denotes the inverse function, not the reciprocal.
• Inverse Secant: A descriptive term synonymous with .

Synonyms

• Inverse secant function: The formal descriptive synonym.
• Arc secant: A less common variant.

Notes

• It is crucial to distinguish or from , which is the reciprocal of the secant, i.e., the cosine: . The notation for the inverse function is a historical convention.

Học thuật

Noun

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

Từ đồng nghĩa

• arc secant
• arcsecant
• inverse secant