Arccos of −√3/2
Arcsin, Arccos, Arctan, Arccot
What is arccos(−√3/2)?
Answer
arccos(−√3/2) =
150° = 5π/6
Range: arccos x is an angle from 0° to 180°, so the answer is unique.
arccos(−√3/2) is the angle α in [0°, 180°] with cos α = −√3/2.
arccos(−√3/2) = 180° − arccos(√3/2) = 180° − 30° = 150°
α = arccos(−√3/2) = 150°
P(cos 150°, sin 150°) = (−√3/2, 1/2)
P lies on the line x = −√3/2 in the upper half of the circle, where sin α ≥ 0; highlighted: cos α = −√3/2.
| Function | Degrees | Radians |
|---|---|---|
| arcsin(−√3/2) | −60° | −π/3 |
| arccos(−√3/2) | 150° | 5π/6 |
| arctan(−√3/2) | ≈ −40.8934° | ≈ −0.7137 |
| arccot(−√3/2) | ≈ 130.8934° | ≈ 2.2845 |
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See Also
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<a href="https://calculat.io/en/number/inverse-trigonometry/arccos---sqrt3-2">Arccos of −√3/2 (Inverse Cosine) in Degrees and Radians</a>Facebook
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![Arccos of −√3/2 (Inverse Cosine) in Degrees and Radians. arccos(−√3/2) = 150° = 5π/6: the angle in [0°, 180°] whose cosine is −√3/2. With the check and the unit circle.](https://calculat.io/en/number/inverse-trigonometry/arccos---sqrt3-2/generated.jpg)
Arccosine of nearby values
| x | arccos x |
|---|---|
| −1 | 180° = π |
| −√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 |