inverse secant

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inverse secant

The student calculates the inverse secant of a value on her calculator.

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.
inverse secant

The student calculates the inverse secant of a value on her calculator.

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

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