Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
inverse cosine
|
| gptkbp:codomain |
[0, π]
|
| gptkbp:complexExtension |
Yes
|
| gptkbp:continuity |
Yes
|
| gptkbp:differentiable |
Yes
|
| gptkbp:domain |
[-1, 1]
|
| gptkbp:evenFunction |
No
|
| gptkbp:expressionInLogarithms |
arccos(x) = -i ln(x + i√(1-x²))
|
| https://www.w3.org/2000/01/rdf-schema#label |
Arccosine
|
| gptkbp:isInverseOf |
gptkb:Cosine_function
|
| gptkbp:isMultivalued |
No
|
| gptkbp:isRealValued |
Yes
|
| gptkbp:monotonic |
Decreasing
|
| gptkbp:notableDerivative |
-1/√(1-x²)
|
| gptkbp:oddFunction |
No
|
| gptkbp:period |
No
|
| gptkbp:principalValueBranch |
[0, π]
|
| gptkbp:range |
[0, π]
|
| gptkbp:relationToArcsin |
arccos(x) + arcsin(x) = π/2
|
| gptkbp:relationToArctan |
arccos(x) = arctan(√(1-x²)/x) for x in (0,1]
|
| gptkbp:relationToCosine |
arccos(cos(x)) = x for x in [0, π]
cos(arccos(x)) = x |
| gptkbp:symbol |
arccos
cos⁻¹ |
| gptkbp:usedIn |
gptkb:geometry
gptkb:mathematics engineering physics trigonometry |
| gptkbp:bfsParent |
gptkb:Cosine_function
|
| gptkbp:bfsLayer |
8
|