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 |
Found an error in the calculation or the information?
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
Share This Calculation
Print
<a href="https://calculat.io/en/number/inverse-trigonometry/arccos--sqrt2-2">Arccos of √2/2 (Inverse Cosine) in Degrees and Radians</a>Facebook
Twitter
Telegram
WhatsApp
Viber
Email
![Arccos of √2/2 (Inverse Cosine) in Degrees and Radians. arccos(√2/2) = 45° = π/4: the angle in [0°, 180°] whose cosine is √2/2. With the check and the unit circle.](https://calculat.io/en/number/inverse-trigonometry/arccos--sqrt2-2/generated.jpg)
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 |