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Arctan (inverse tangent, tan⁻¹) returns the angle whose tangent equals the input. Unlike arcsin and arccos, the domain is all real numbers (−∞, +∞).
Fórmula
θ = arctan(x) where tan(θ) = x
- x
- input value (tangent) — any real number (−∞, +∞)
- θ
- angle result (degrees or radians)
Guia passo a passo
- 1arctan(x) returns θ where tan(θ) = x
- 2Domain: all real numbers
- 3Range: (−90°, 90°) or (−π/2, π/2)
- 4arctan(1) = 45°, arctan(0) = 0°
Exemplos resolvidos
Entrada
arctan(1)
Resultado
45° or π/4 radians
Entrada
arctan(√3)
Resultado
60° or π/3 radians
Entrada
arctan(−1)
Resultado
−45°
Perguntas frequentes
What is the domain and range of arctan?
Domain: all real numbers. Range: (−90°, 90°) or (−π/2, π/2) radians.
Why does arctan have a larger domain than arcsin and arccos?
Tangent is defined for all angles except ±90°, so its inverse also accepts all real values.
What is atan2 and how does it differ from arctan?
atan2(y, x) takes two arguments and returns the angle in the correct quadrant. arctan only uses one value.
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