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Arcsin (inverse sine, sin⁻¹) returns the angle whose sine equals the input value. The output range is [−90°, 90°] or [−π/2, π/2] radians.
Fórmula
θ = arcsin(x) where sin(θ) = x
- x
- input value (sine) — must be in range [−1, 1]
- θ
- angle result (degrees or radians)
Guia passo a passo
- 1arcsin(x) returns θ where sin(θ) = x
- 2Domain: x ∈ [−1, 1]
- 3Range: [−90°, 90°]
- 4arcsin(0.5) = 30°, arcsin(1) = 90°
Exemplos resolvidos
Entrada
arcsin(0.5)
Resultado
30° or π/6 radians
Entrada
arcsin(1)
Resultado
90° or π/2 radians
Entrada
arcsin(−0.5)
Resultado
−30°
Perguntas frequentes
What is the domain and range of arcsin?
Domain: [−1, 1]. Range: [−90°, 90°] or [−π/2, π/2] radians.
Why does arcsin only return angles up to 90°?
The principal range of arcsin is restricted to avoid ambiguity, since multiple angles can have the same sine value.
How is arcsin related to arccsc (arc cosecant)?
arcsin(x) = arccsc(1/x), just like sin and csc are reciprocals.
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