Arcsin of −1/2
Arcsin, Arccos, Arctan, Arccot
What is arcsin(−1/2)?
Answer
arcsin(−1/2) =
−30° = −π/6
Range: arcsin x is an angle from −90° to 90°, so the answer is unique.
−1/2 = −0.5.
arcsin(−1/2) is the angle α in [−90°, 90°] with sin α = −1/2.
arcsin(−1/2) = −arcsin(1/2) = −30°
sin(−30°) = −1/2 ✓
α = arcsin(−1/2) = −30°
P(cos(−30°), sin(−30°)) = (√3/2, −1/2)
P lies on the line y = −1/2 in the right half of the circle, where cos α ≥ 0; highlighted: sin α = −1/2.
| Function | Degrees | Radians |
|---|---|---|
| arcsin(−1/2) | −30° | −π/6 |
| arccos(−1/2) | 120° | 2π/3 |
| arctan(−1/2) | ≈ −26.5651° | ≈ −0.4636 |
| arccot(−1/2) | ≈ 116.5651° | ≈ 2.0344 |
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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---1-2">Arcsin of −1/2 (Inverse Sine) in Degrees and Radians</a>Facebook
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![Arcsin of −1/2 (Inverse Sine) in Degrees and Radians. arcsin(−1/2) = −30° = −π/6: the angle in [−90°, 90°] whose sine is −1/2. With the check and the unit circle.](https://calculat.io/en/number/inverse-trigonometry/arcsin---1-2/generated.jpg)
Arcsine of nearby values
| x | arcsin x |
|---|---|
| −√3/2 | −60° = −π/3 |
| −4/5 | ≈ −53.1301° |
| −√2/2 | −45° = −π/4 |
| −1/2 | −30° = −π/6 |
| −0.3 | ≈ −17.4576° |
| 0 | 0° = 0 |
| 0.1 | ≈ 5.7392° |