Arccos of √2/2
Arcsin, Arccos, Arctan, Arccot
What is arccos(√2/2)?
Answer
arccos(√2/2) =
45° = π/4
Range: arccos x is an angle from 0° to 180°, so the answer is unique.
arccos(√2/2) is the angle α in [0°, 180°] with cos α = √2/2.
α = arccos(√2/2) = 45°
P(cos 45°, sin 45°) = (√2/2, √2/2)
P lies on the line x = √2/2 in the upper half of the circle, where sin α ≥ 0; highlighted: cos α = √2/2.
| Function | Degrees | Radians |
|---|---|---|
| arcsin(√2/2) | 45° | π/4 |
| arccos(√2/2) | 45° | π/4 |
| arctan(√2/2) | ≈ 35.2644° | ≈ 0.6155 |
| arccot(√2/2) | ≈ 54.7356° | ≈ 0.9553 |
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 |
|---|---|
| 0.65 | ≈ 49.4584° |
| 2/3 | ≈ 48.1897° |
| 0.7 | ≈ 45.5730° |
| √2/2 | 45° = π/4 |
| 3/4 | ≈ 41.4096° |
| 4/5 | ≈ 36.8699° |
| √3/2 | 30° = π/6 |
FAQ
What is arccos(√2/2)?
arccos(√2/2) = 45° = π/4
How to find arccos(√2/2) from a table of cosines?
Look in the table for the angle α in [0°, 180°] with cos α = √2/2: it is 45°, or π/4 in radians.
Why does a calculator show 0.7854 for arccos(√2/2)?
The calculator is in radian mode (RAD) and gives the angle in radians: arccos(√2/2) = π/4 ≈ 0.7854 rad. In degrees (DEG) it is 45°.
See Also
- Arccos of 1/5 (Inverse Cosine) in Degrees and Radians
- 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 √3/2 (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
- Арккосинус √2/2 (arccos √2/2) в градусах и радианах
- Arcocoseno de √2/2 (arccos √2/2) en grados y radianes
- Arco cosseno de √2/2 (arccos √2/2) em graus e radianos