Arcsin of √2/2
Arcsin, Arccos, Arctan, Arccot
What is arcsin(√2/2)?
Answer
arcsin(√2/2) =
45° = π/4
Range: arcsin x is an angle from −90° to 90°, so the answer is unique.
arcsin(√2/2) is the angle α in [−90°, 90°] with sin α = √2/2.
α = arcsin(√2/2) = 45°
P(cos 45°, sin 45°) = (√2/2, √2/2)
P lies on the line y = √2/2 in the right half of the circle, where cos α ≥ 0; highlighted: sin 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 |
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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/arcsin--sqrt2-2">Arcsin of √2/2 (Inverse Sine) in Degrees and Radians</a>Facebook
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![Arcsin of √2/2 (Inverse Sine) in Degrees and Radians. arcsin(√2/2) = 45° = π/4: the angle in [−90°, 90°] whose sine is √2/2. With the check and the unit circle.](https://calculat.io/en/number/inverse-trigonometry/arcsin--sqrt2-2/generated.jpg)
Arcsine of nearby values
| x | arcsin x |
|---|---|
| 3/5 | ≈ 36.8699° |
| 2/3 | ≈ 41.8103° |
| 0.7 | ≈ 44.4270° |
| √2/2 | 45° = π/4 |
| 3/4 | ≈ 48.5904° |
| 4/5 | ≈ 53.1301° |
| √3/2 | 60° = π/3 |