Arccos of √3/2
Arcsin, Arccos, Arctan, Arccot
What is arccos(√3/2)?
Answer
arccos(√3/2) =
30° = π/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.
α = arccos(√3/2) = 30°
P(cos 30°, sin 30°) = (√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) | 30° | π/6 |
| arctan(√3/2) | ≈ 40.8934° | ≈ 0.7137 |
| arccot(√3/2) | ≈ 49.1066° | ≈ 0.8571 |
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
Arccosine of nearby values
| x | arccos x |
|---|---|
| √2/2 | 45° = π/4 |
| 3/4 | ≈ 41.4096° |
| 4/5 | ≈ 36.8699° |
| √3/2 | 30° = π/6 |
| 0.9 | ≈ 25.8419° |
| 12/13 | ≈ 22.6199° |
| 1 | 0° = 0 |
FAQ
What is arccos(√3/2)?
arccos(√3/2) = 30° = π/6
How to find arccos(√3/2) from a table of cosines?
Look in the table for the angle α in [0°, 180°] with cos α = √3/2: it is 30°, or π/6 in radians.
Why does a calculator show 0.5236 for arccos(√3/2)?
The calculator is in radian mode (RAD) and gives the angle in radians: arccos(√3/2) = π/6 ≈ 0.5236 rad. In degrees (DEG) it is 30°.
See Also
- Arccos of 2 (Inverse Cosine) in Degrees and Radians
- Arccos of 2/3 (Inverse Cosine) in Degrees and Radians
- Arccos of 2/5 (Inverse Cosine) in Degrees and Radians
- Arccos of 3/4 (Inverse Cosine) in Degrees and Radians
- Arccos of 3/5 (Inverse Cosine) in Degrees and Radians
- Arccos of 4/5 (Inverse Cosine) in Degrees and Radians
- Arccos of 4/7 (Inverse Cosine) in Degrees and Radians
- Arccos of 12/13 (Inverse Cosine) in Degrees and Radians
- Arccos of 60 (Inverse Cosine) in Degrees and Radians
- Arccos of √2/2 (Inverse Cosine) in Degrees and Radians
- Arccos of √3/3 (Inverse Cosine) in Degrees and Radians
- Arccot of −1 (Inverse Cotangent) in Degrees and Radians
- Arccot of −2 (Inverse Cotangent) in Degrees and Radians
- Arccot of −√3 (Inverse Cotangent) in Degrees and Radians
- Arccot of −√3/3 (Inverse Cotangent) in Degrees and Radians
- Arccot of 0 (Inverse Cotangent) in Degrees and Radians
- Arccot of 0.3 (Inverse Cotangent) in Degrees and Radians
- Arccot of 1 (Inverse Cotangent) in Degrees and Radians
- Arccot of 1/2 (Inverse Cotangent) in Degrees and Radians
- Arccot of 2 (Inverse Cotangent) in Degrees and Radians
- Арккосинус √3/2 (arccos √3/2) в градусах и радианах
- Arcocoseno de √3/2 (arccos √3/2) en grados y radianes
- Arco cosseno de √3/2 (arccos √3/2) em graus e radianos