Definition
The inverse of the sine function. If the sine of an angle equals a given value, the arc sine of that value returns the original angle. Written as sin⁻¹ or arcsin.
Plain English
A math operation that works backwards from sine. Sine takes an angle and gives a number; arc sine takes that number and gives back the angle.
Context Anchor
Seen in aviation math, especially when a calculation uses a measured ratio to find an angle.
Derivation
From Latin arcus, meaning 'arc' or 'bow.' In trigonometry, an angle corresponds to an arc on a circle, so 'arc sine' literally means 'the arc (angle) whose sine is...' This naming reminds you the result is an angle, not a ratio.
Why Pilots Care
Pilots rarely calculate arc sine by hand, but it underlies wind correction angle problems, glide path geometry, and many performance formulas. Knowing what the function returns helps when interpreting results from an E6B, calculator, or flight planning software.
Intuition Check
Arc sine is not a curved flight path. It is a math function used to find an angle from a sine value.
Example Sentence 1
To find the wind correction angle, the pilot's calculator used arc sine to convert the crosswind ratio back into degrees.
Example Sentence 2
During flight planning the navigator applied arc sine to the sine of the drift angle to recover the required heading correction.