arc secant
Definition
- Noun:
- The inverse function of the secant: The
arc secantis 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 secantof 2. - The value of
arc secantof 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.
Noun
-
the inverse function of the secant; the angle that has a secant equal to a given number
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