Arccos of −1/2
Arcsin, Arccos, Arctan, Arccot
What is arccos(−1/2)?
Answer
arccos(−1/2) =
120° = 2π/3
Range: arccos x is an angle from 0° to 180°, so the answer is unique.
−1/2 = −0.5.
arccos(−1/2) is the angle α in [0°, 180°] with cos α = −1/2.
arccos(−1/2) = 180° − arccos(1/2) = 180° − 60° = 120°
α = arccos(−1/2) = 120°
P(cos 120°, sin 120°) = (−1/2, √3/2)
P lies on the line x = −1/2 in the upper half of the circle, where sin α ≥ 0; highlighted: cos 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/arccos---1-2">Arccos of −1/2 (Inverse Cosine) in Degrees and Radians</a>Facebook
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![Arccos of −1/2 (Inverse Cosine) in Degrees and Radians. arccos(−1/2) = 120° = 2π/3: the angle in [0°, 180°] whose cosine is −1/2. With the check and the unit circle.](https://calculat.io/en/number/inverse-trigonometry/arccos---1-2/generated.jpg)
Arccosine of nearby values
| x | arccos x |
|---|---|
| −√3/2 | 150° = 5π/6 |
| −4/5 | ≈ 143.1301° |
| −√2/2 | 135° = 3π/4 |
| −1/2 | 120° = 2π/3 |
| −0.3 | ≈ 107.4576° |
| 0 | 90° = π/2 |
| 0.1 | ≈ 84.2608° |