arc sine: meaning, definition, pronunciation and examples
C2Technical / Academic
Quick answer
What does “arc sine” mean?
The inverse function of the sine.
Audio
Pronunciation
Definition
Meaning and Definition
The inverse function of the sine; for a given number between -1 and 1, it returns the angle (in radians or degrees) whose sine is that number.
A fundamental trigonometric function used to find an angle when the ratio of the opposite side to the hypotenuse in a right-angled triangle is known. It is a key concept in mathematics, physics, engineering, and computer graphics.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. Spelling conventions for the abbreviation may follow the general pattern of the region (e.g., 'arcsine' as a single word is common in both).
Connotations
None beyond the technical mathematical meaning.
Frequency
Equally rare in general discourse in both regions, used with identical frequency in technical fields.
Grammar
How to Use “arc sine” in a Sentence
the arc sine of [number/expression]arc sine([argument])compute arc sine forVocabulary
Collocations
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core terminology in trigonometry, calculus, and engineering mathematics courses.
Everyday
Extremely rare; would only appear in highly specific educational or hobbyist contexts.
Technical
Essential in fields requiring trigonometric calculations, signal processing, physics (especially wave mechanics), and computer graphics programming.
Vocabulary
Synonyms of “arc sine”
Strong
Neutral
Weak
Vocabulary
Antonyms of “arc sine”
Watch out
Common Mistakes When Using “arc sine”
- Confusing it with the reciprocal of sine (cosecant).
- Forgetting to restrict the input domain to [-1, 1].
- Using degrees when the context requires radians or vice versa.
- Misspelling as 'arc sin' or 'arcsin' without understanding it's the same.
FAQ
Frequently Asked Questions
Both 'arc sine' (open) and 'arcsine' (closed) are accepted, with the closed form being very common in technical writing. 'Arcsin' is the standard abbreviation.
Arc sine is the inverse function (angle from ratio). Cosecant (csc) is the reciprocal function (1/sin) of the sine (ratio from angle). They are completely different operations.
The sine function is not one-to-one over all angles. Restricting the output (the principal value) makes the arc sine a proper function, giving a single, unique answer for each input.
No. Since the sine of any angle is always between -1 and 1, the domain (allowed inputs) for the arc sine function is only the numbers in the interval [-1, 1].
The inverse function of the sine.
Arc sine is usually technical / academic in register.
Arc sine: in British English it is pronounced /ˌɑːk ˈsaɪn/, and in American English it is pronounced /ˌɑːrk ˈsaɪn/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think: ARC goes BACK. The sine gives you the ratio from an angle. The ARC sine gives you the ANGLE back from the ratio.
Conceptual Metaphor
UNDOING / REVERSAL (It is the 'undo' operation for the sine function).
Practice
Quiz
What is the principal value range for the arc sine function in radians?