Enter any value between -1 and 1 into the Arcsin Calculator and get the inverse sine (arcsin) as both an angle in degrees and an angle in radians. Choose whether your input represents a decimal or a common fraction — the calculator handles both. Results follow the principal value range of −90° to 90° (−π/2 to π/2).
Angle in Degrees
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Angle in Radians
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Angle in Terms of π
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Expression
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Arcsin is the inverse function of the sine function. While sin(θ) gives you the ratio of the opposite side to the hypotenuse for an angle θ, arcsin(x) gives you the angle whose sine equals x. Its output is restricted to the principal value range of −90° to 90° (or −π/2 to π/2 radians).
The domain of arcsin is [−1, 1], meaning you can only enter values between −1 and 1 inclusive. Sine values can never exceed 1 or be less than −1, so inputs outside this range are mathematically undefined for the real number system.
To find the arcsine, apply the formula: angle = arcsin(x) = sin⁻¹(x). For example, arcsin(0.5) = 30° because sin(30°) = 0.5. On a scientific calculator, use the sin⁻¹ or asin button. This calculator does it for you automatically and shows the result in both degrees and radians.
Degrees and radians are two units for measuring angles. The same angle can be expressed as 30° or π/6 radians (≈ 0.5236 rad). Radians are the standard unit in mathematics and physics, while degrees are more common in everyday contexts. To convert: degrees = radians × (180/π).
The notation sin⁻¹(x) is an alternative way to write arcsin(x), where the superscript −1 denotes the inverse function rather than a reciprocal. This can be confusing, since sin²(x) means (sin x)², but sin⁻¹(x) does NOT mean 1/sin(x) — that would be csc(x). Many mathematicians prefer 'arcsin' to avoid this ambiguity.
The domain of arcsin is [−1, 1] — only values within this interval are valid inputs. The range (output) is [−π/2, π/2] in radians, or equivalently [−90°, 90°] in degrees. This restricted range ensures arcsin is a proper function with one unique output per input.
If you know the length of the side opposite an angle and the hypotenuse of a right triangle, you can find the angle using arcsin. For example, if the opposite side is 3 and the hypotenuse is 6, then sin(θ) = 3/6 = 0.5, so θ = arcsin(0.5) = 30°. This makes arcsin essential in geometry and trigonometry.
No. Arcsin (sin⁻¹) is the inverse function of sine — it returns an angle. Cosecant (csc) is the reciprocal of sine: csc(x) = 1/sin(x). They are completely different operations. Arcsin takes a ratio and returns an angle, while cosecant takes an angle and returns a ratio.