arcsine

Angle from ratio

Arcsine is the inverse of the sine function in trigonometry—given a ratio, it returns the angle that would produce that ratio.

If the sine of 30° is 0.5, then the arcsine of 0.5 is 30°.

Written as arcsin or sin⁻¹ in mathematical notation: arcsin(0.5) = 30°.

The function is essential for solving triangles and appears throughout physics and engineering.

function

inverse function

Function undoing another function

domainArea of control
rangeExtent of variation
inputData received for processing

output · mapping · principal value · one-to-one · composition · graph · curve · monotonic · bounded · continuous

angle

radians

Angle measurement units

degreesUnits of measurement
principal valueCanonical multivalued function output
quadrantFourth of a circle

rotation · arc length · central angle · subtended · measurement · conversion · calculator · evaluation

trigonometry

cosine

Ratio in triangle math

arccosineInverse of cosine function
tangentLine touching curve once
secantTrig ratio, 1/cos

cosecant · cotangent · hypotenuse · opposite · adjacent · unit circle · periodic · amplitude · frequency · phase

application

signal processing

Mathematical manipulation of waveforms

physicsScience of matter and energy
engineeringDesigning functional systems scientifically
navigationDetermining position and course

acoustics · optics · harmonic motion · projectile motion · astronomy · geodesy · computer graphics · interpolation

Categories

trigonometrycosine, tangent, secant, cosecant, cotangent
inverse functionsarccos, arctan, arccosine, arccot, logarithm
math functionsabs, cosine, add, tangent, subtract

Opposites

mathematical inverse function

arcsinesine

Opposite over hypotenuse

sin · sine function

complementary inverse trigonometric function

arcsinearccosine

Inverse of cosine function

arccos · arctangent · arctan

Family

Familiarity: Top 500,000
Profile: Used worldwide · Timeless · Abstract · Rated G