Definition

1. Noun:
   • The inverse function of the secant: A mathematical function that, for a given number, returns the angle whose secant is that number. It is the function that reverses, or "undoes," the action of the secant function.

Usage

• The inverse secant is used to find an angle when the value of its secant is known.
• It is often denoted as or .
• Its principal value range is typically , excluding (where the secant function is undefined).

Examples

• Noun:
  • To solve for the angle θ in the equation sec(θ) = 2, you must use the inverse secant.
  • The value of arcsec(√2) is π/4 radians, because sec(π/4) = √2.

Advanced Usage

• Domain and Range: The domain of the inverse secant function is . Its range (principal values) is .
• Derivative: The derivative of the inverse secant function is .

Variants and Related Words

• arcsecant (n): A synonym for inverse secant, denoted as .
• sec⁻¹ (n): The standard notation for the inverse secant function.
• Inverse trigonometric function (n): The general category of functions that includes inverse secant, inverse sine, inverse cosine, etc.

Synonyms

• arcsecant
• arcsec

Related Concepts (Not Phrasal Verbs or Idioms)

• Secant function (sec): The trigonometric function whose inverse is the inverse secant.
• Inverse cosecant (arccsc): The inverse function of the cosecant.
• Principal value: The specific, conventionally chosen output range for an inverse trigonometric function.

Noun

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