arc tangent: meaning, definition, pronunciation and examples
LowTechnical/Formal
Quick answer
What does “arc tangent” mean?
The inverse trigonometric function of tangent.
Audio
Pronunciation
Definition
Meaning and Definition
The inverse trigonometric function of tangent; the angle whose tangent is a given number.
In mathematics and computing, a function that returns the principal value of the angle (in radians or degrees) from the ratio of the opposite side to the adjacent side in a right triangle. Also used in complex analysis and engineering.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling conventions follow general patterns: 'arc tangent' (two words) is common in both, though 'arctangent' (one word) is also accepted. The abbreviation 'arctan' is universal.
Connotations
Purely technical term with identical connotations in both varieties.
Frequency
Equally low frequency in specialised mathematical/engineering contexts in both regions.
Grammar
How to Use “arc tangent” in a Sentence
arc tangent of [number/variable]compute the arc tangentthe arc tangent function returnsVocabulary
Collocations
Examples
Examples of “arc tangent” in a Sentence
verb
British English
- To find the angle, you must arc-tangent the ratio.
- The software arc-tangents the value automatically.
American English
- You need to arctangent that quotient to get the phase.
- The processor arctangents the input in one cycle.
adverb
British English
- The value was computed arc-tangentially.
- It behaves arc-tangently near the asymptote.
American English
- The signal was processed arctangentially.
- The curve increases arctangently.
adjective
British English
- The arc-tangent transformation is useful here.
- We applied an arc-tangent scaling to the data.
American English
- The arctangent function is built into the library.
- Use the arctangent operation for this calculation.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Used in mathematics, physics, engineering, and computer science courses and publications.
Everyday
Extremely rare outside educational or technical contexts.
Technical
Core term in trigonometry, calculus, signal processing, robotics (for calculating angles from coordinates), and computer graphics.
Watch out
Common Mistakes When Using “arc tangent”
- Confusing 'arc tangent' (inverse function) with 'cotangent' (reciprocal function, 1/tan).
- Forgetting to specify the output range or units (radians vs degrees).
- Misspelling as 'arch tangent'.
FAQ
Frequently Asked Questions
No, they are completely different. Arc tangent (arctan) is the inverse function of tangent. Cotangent (cot) is the reciprocal function (1/tan).
Typically, 'arctan' denotes the principal value function, while 'Arctan' can sometimes denote the multi-valued inverse relation in advanced mathematics, but in most practical contexts, they are used interchangeably.
The 'arc' refers to the arc (and thus the angle) of a unit circle. The function gives the arc (angle) whose tangent is a specific value.
Common applications include calculating the angle of a slope in construction, determining the direction of a vector in physics or computer graphics, and in signal processing for phase detection.
The inverse trigonometric function of tangent.
Arc tangent is usually technical/formal in register.
Arc tangent: in British English it is pronounced /ˌɑːk ˈtændʒənt/, and in American English it is pronounced /ˌɑːrk ˈtændʒənt/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None”
Learning
Memory Aids
Mnemonic
ARC TANGENT: ARCH back to the ANGLE. It takes you back (inversely) from a tangent ratio to the original angle.
Conceptual Metaphor
A REVERSAL MACHINE / A LOOKUP TABLE: It reverses the process of the tangent function, looking up the angle that corresponds to a given ratio.
Practice
Quiz
What is the principal value range for the arc tangent function in radians?