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.
arcsin(−√2/2) = −arcsin(√2/2) = −45°
sin(−45°) = −√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) | 135° | 3π/4 |
| arctan(−√2/2) | ≈ −35.2644° | ≈ −0.6155 |
| arccot(−√2/2) | ≈ 125.2644° | ≈ 2.1863 |
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See Also
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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 |
|---|---|
| −1 | −90° = −π/2 |
| −√3/2 | −60° = −π/3 |
| −4/5 | ≈ −53.1301° |
| −√2/2 | −45° = −π/4 |
| −1/2 | −30° = −π/6 |
| −0.3 | ≈ −17.4576° |
| 0 | 0° = 0 |