如何计算Arctan
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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 (−∞, +∞).
公式
θ = arctan(x) where tan(θ) = x
- x
- input value (tangent) — any real number (−∞, +∞)
- θ
- angle result (degrees or radians)
分步指南
- 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°
例题解析
输入
arctan(1)
结果
45° or π/4 radians
输入
arctan(√3)
结果
60° or π/3 radians
输入
arctan(−1)
结果
−45°
常见问题
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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