Arcsin of √3/2
Arcsin, Arccos, Arctan, Arccot
What is arcsin(√3/2)?
Answer
arcsin(√3/2) =
60° = π/3
Range: arcsin x is an angle from −90° to 90°, so the answer is unique.
arcsin(√3/2) is the angle α in [−90°, 90°] with sin α = √3/2.
α = arcsin(√3/2) = 60°
P(cos 60°, sin 60°) = (1/2, √3/2)
P lies on the line y = √3/2 in the right half of the circle, where cos α ≥ 0; highlighted: sin α = √3/2.
| Function | Degrees | Radians |
|---|---|---|
| arcsin(√3/2) | 60° | π/3 |
| arccos(√3/2) | 30° | π/6 |
| arctan(√3/2) | ≈ 40.8934° | ≈ 0.7137 |
| arccot(√3/2) | ≈ 49.1066° | ≈ 0.8571 |
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See Also
- Sin, Cos, Tan, Cot of an Angle - Exact value in square roots and the decimal, with reduction to an acute angle on the unit circle
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
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<a href="https://calculat.io/en/number/inverse-trigonometry/arcsin--sqrt3-2">Arcsin of √3/2 (Inverse Sine) in Degrees and Radians</a>Facebook
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![Arcsin of √3/2 (Inverse Sine) in Degrees and Radians. arcsin(√3/2) = 60° = π/3: the angle in [−90°, 90°] whose sine is √3/2. With the check and the unit circle.](https://calculat.io/en/number/inverse-trigonometry/arcsin--sqrt3-2/generated.jpg)
Arcsine of nearby values
| x | arcsin x |
|---|---|
| √2/2 | 45° = π/4 |
| 3/4 | ≈ 48.5904° |
| 4/5 | ≈ 53.1301° |
| √3/2 | 60° = π/3 |
| 0.9 | ≈ 64.1581° |
| 1 | 90° = π/2 |
| 3/2 | does not exist |