Arccos of −√2/2
Arcsin, Arccos, Arctan, Arccot
What is arccos(−√2/2)?
Answer
arccos(−√2/2) =
135° = 3π/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.
arccos(−√2/2) = 180° − arccos(√2/2) = 180° − 45° = 135°
α = arccos(−√2/2) = 135°
P(cos 135°, sin 135°) = (−√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) | 135° | 3π/4 |
| arctan(−√2/2) | ≈ −35.2644° | ≈ −0.6155 |
| arccot(−√2/2) | ≈ 125.2644° | ≈ 2.1863 |
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 |
|---|---|
| −1 | 180° = π |
| −√3/2 | 150° = 5π/6 |
| −4/5 | ≈ 143.1301° |
| −√2/2 | 135° = 3π/4 |
| −1/2 | 120° = 2π/3 |
| −0.3 | ≈ 107.4576° |
| 0 | 90° = π/2 |
FAQ
What is arccos(−√2/2)?
arccos(−√2/2) = 135° = 3π/4
Why is arccos(−√2/2) = 135° and not −45°?
The range of arccos is from 0° to 180°: there are no negative angles in it. A negative x gives an angle greater than 90°: arccos(−√2/2) = 180° − arccos(√2/2) = 180° − 45° = 135°. The angle −45° does not fit: cos(−α) = cos α, so its cosine is positive.
Why does a calculator show 2.3562 for arccos(−√2/2)?
The calculator is in radian mode (RAD) and gives the angle in radians: arccos(−√2/2) = 3π/4 ≈ 2.3562 rad. In degrees (DEG) it is 135°.
See Also
- Arccos of −0.3 (Inverse Cosine) in Degrees and Radians
- Arccos of −1 (Inverse Cosine) in Degrees and Radians
- Arccos of −1/2 (Inverse Cosine) in Degrees and Radians
- Arccos of −4/5 (Inverse Cosine) in Degrees and Radians
- Arccos of −√3/2 (Inverse Cosine) in Degrees and Radians
- Arccos of 0 (Inverse Cosine) in Degrees and Radians
- Arccos of 0.1 (Inverse Cosine) in Degrees and Radians
- Arccos of 0.3 (Inverse Cosine) in Degrees and Radians
- Arccos of 0.7 (Inverse Cosine) in Degrees and Radians
- Arccos of 0.9 (Inverse Cosine) in Degrees and Radians
- Arccos of 0.14 (Inverse Cosine) in Degrees and Radians
- Arccos of 0.55 (Inverse Cosine) in Degrees and Radians
- Arccos of 0.65 (Inverse Cosine) in Degrees and Radians
- Arccos of 1 (Inverse Cosine) 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