arc secant

Thân thiện

The student calculates the arc secant of a value on the graph.

Definition

1. Noun:
   • The inverse function of the secant: The arc secant is a mathematical function that, for a given number, returns the angle whose secant is that number. It is the inverse operation of the secant function.

Usage

• The function is used to find an angle when the value of the secant of that angle is known.
• It is typically denoted as or .
• The output (the angle) is usually expressed in radians or degrees.

Examples

• Noun:
  • To solve for the angle theta, you must compute the arc secant of 2.
  • The value of arc secant of a number greater than or equal to 1 lies between 0 and π radians (excluding π/2).

Advanced Usage

• Principal Value: The function is defined with a specific range, called its principal branch, to make it a proper function. For real numbers, this is often excluding .
• Relation to Arc Cosine: For , the of is related to the arc cosine by the identity: .

Variants and Related Words

• arcsec: A common abbreviation for .
  • Calculate arcsec(√2).
• inverse secant: A synonymous term for .
• sec⁻¹: A standard notation for the function.

Synonyms

• Inverse secant: The direct synonym for .

Notes

• The is a trigonometric function, specifically an inverse trigonometric function.
• Its domain is the set of real numbers such that .
• It is less commonly used in basic trigonometry than the arc sine or arc cosine.

Học thuật

Noun

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

Từ đồng nghĩa

• arcsecant
• arcsec
• inverse secant