Definition
A trigonometric function that returns the angle whose tangent is a given number. If the tangent of an angle equals a certain ratio (opposite side divided by adjacent side in a right triangle), the arc tangent of that ratio gives back the angle itself. Written as arctan, tan⁻¹, or atan.
Plain English
A math operation that works backwards from a ratio to find the angle that produced it. If you know how steep something is as a number, arc tangent tells you the angle of that steepness in degrees.
Context Anchor
Seen in navigation, performance, and instrument discussions when an angle is calculated from two measured distances or rates.
Derivation
From Latin arcus meaning 'bow' or 'arc,' and tangent from Latin tangere meaning 'to touch.' In trigonometry, an angle corresponds to an arc on a circle, so 'arc tangent' literally means 'the arc (angle) whose tangent is...' — it reverses the tangent function back to the angle.
Why Pilots Care
Pilots rarely calculate arc tangent by hand, but it sits behind the scenes in flight computers, GPS course calculations, glideslope geometry, and wind triangle solutions. Understanding what it does helps when reading technical material on navigation or aircraft performance.
Grounding Statement
If you know how much something goes up or down compared with how far it goes forward, arc tangent gives the angle of that path.
Intuition Check
Arc tangent is not a physical arc in the sky and not a line just touching a curve. Here it is a math function that finds an angle from a ratio.
Example Sentence 1
To find the climb angle from a known rise and run, you take the arc tangent of the rise divided by the run.
Example Sentence 2
A pilot used the arc tangent of the distance ratio to compute the precise heading change needed.