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Inverse Trig Functions Calculator

Find the angle whose sine, cosine, or tangent equals a given value, expressed in both degrees and radians.

Function

Pick the inverse trigonometric function
arcsin and arccos require x between -1 and 1
Angle
30°

Principal value angle in degrees

Angle (radians)
0.523599 rad
Angle (degrees)
30 °
Input value
0.5
Principal range
[-90°, 90°] / [-π/2, π/2]
Parent wave — the inverse function returns the angle where this wave equals the input x
Step by step
  1. 1

    arcsin(x) in radians

    arcsin(0.5) = 0.523599
    Principal-value angle in radians.
  2. 2

    Convert to degrees

    0.523599 × 180 ÷ π = 30
Results are estimates for general information only and are not professional advice — always verify important results independently before relying on them. Read the full disclaimer.
Quick answer

How does this calculator work?

Pick arcsin, arccos, or arctan and enter a value to get the principal angle in degrees and radians. Arcsin and arccos need inputs in [-1, 1]; arctan accepts any number. The result is converted using degrees = radians × 180 / π and reported within each function’s principal value range.

Formula
θ = arcsin(x) or arccos(x) or arctan(x); degrees = radians × 180 / π
How this is calculated

Choose an inverse function (arcsin, arccos, or arctan) and enter a value x. The calculator evaluates the principal value of the chosen inverse trigonometric function using the standard library routines Math.asin, Math.acos, and Math.atan, which return an angle in radians.

The radian result is converted to degrees with the relation degrees = radians × 180 / π. For arcsin the principal range is [-90°, 90°] ([-π/2, π/2]); for arccos it is [0°, 180°] ([0, π]); and for arctan it is (-90°, 90°) ((-π/2, π/2)). Each inverse function returns only one angle from this principal range even though sine, cosine, and tangent are periodic and would otherwise have infinitely many matching angles.

A key constraint: arcsin and arccos are only defined for inputs in the closed interval [-1, 1], because sine and cosine never exceed that range. Values outside [-1, 1] are rejected. Arctan accepts any real number, since the tangent function spans all real values.

Frequently asked questions

Sine and cosine of any real angle always fall in [-1, 1], so there is no angle whose sine or cosine is outside that range. Inputs beyond it are undefined and are rejected.

Trigonometric functions are periodic, so infinitely many angles map to the same value. Inverse functions return just the principal value from a standard restricted range to keep the result unique.

Multiply the radian value by 180 and divide by π (about 3.14159). For example, 0.5236 rad × 180 / π ≈ 30°.

Also known as

inverse trig
arcsin arccos arctan
inverse sine
inverse cosine
inverse tangent
inverse trig calculator
arc functions

APA

TG we-Calculate Editorial Team. (2026). Inverse Trig Functions Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/inverse-trig-functions-calculator

Chicago

TG we-Calculate Editorial Team. "Inverse Trig Functions Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/inverse-trig-functions-calculator.

IEEE

TG we-Calculate Editorial Team, "Inverse Trig Functions Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/inverse-trig-functions-calculator

BibTeX

@misc{wecalculate_inverse_trig_functions_calculator, title = {Inverse Trig Functions Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/inverse-trig-functions-calculator}}, year = {2026}, note = {TG we-Calculate} }

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