arccos
Học thuậtThân thiện
Definition
- Noun:
- The inverse function of the cosine:
arccosis a trigonometric function that returns the angle whose cosine is a given number. It is the principal value of the inverse cosine function.
Usage
- is used in mathematics, physics, and engineering to find an angle when the cosine of that angle is known.
- The input value (the cosine) must be between -1 and 1, inclusive. The output (the angle) is typically given in radians, ranging from 0 to π (0 to 180 degrees).
- It is commonly written as or .
Examples
- Noun:
- If cos(θ) = 0.5, then θ = arccos(0.5) = π/3 radians (or 60 degrees).
- To find the angle in the triangle, we calculated the arccos of the adjacent side divided by the hypotenuse.
Advanced Usage
- Principal Value: The function is defined to return a single, specific value (the principal value) for each input to make it a proper function. For a real number where -1 ≤ x ≤ 1, is the unique angle in the interval [0, π] such that cos(y) = x.
- Relation to Arc Cosine: The name "arccos" is an abbreviation of "arcus cosine," meaning "the arc whose cosine is" the given number.
Variants and Related Words
- arccosine (n): A full, alternative name for . It means the same thing.
- The arccosine of 0 is π/2.
- inverse cosine (n): A descriptive term synonymous with .
- The inverse cosine function is denoted as cos⁻¹.
- acos (n): A common abbreviation used in programming languages and calculators.
- In the code, use the
acos()function to compute the angle.
Synonyms
- inverse cosine: The function that undoes the cosine operation.
- cos⁻¹: The standard mathematical notation for the inverse cosine function.
Related Phrases/Concepts
- Domain and Range: A key concept when using . Its domain is [-1, 1] and its range is [0, π] (in radians).
- Trigonometric Identity: is related to other inverse functions. For example, arccos(x) = π/2 - arcsin(x) for x in [-1, 1].
Noun
- the inverse function of the cosine; the angle that has a cosine equal to a given number