- What is arctan?
- Arctan (also written arctangent, tan⁻¹, or atan) is the inverse of the tangent function. arctan(x) returns the angle whose tangent is x. Because tangent repeats every 180°, arctan returns only the principal value — the answer in the range (-90°, 90°) or (-π/2, π/2).
- What's the range of arctan?
- (-90°, 90°) in degrees, or (-π/2, π/2) in radians. The endpoints are never reached — arctan approaches them asymptotically as x approaches ±∞. arctan(1×10¹⁵) returns 89.99999...°, not exactly 90°.
- What's the difference between arctan and atan2?
- arctan takes one argument (a ratio y/x) and always returns an angle in the principal range (-90°, 90°). atan2 takes two arguments (y and x separately) and returns an angle in the full range (-180°, 180°), correctly handling all four quadrants. Use atan2 when you have a point on a plane; use arctan when you only have the ratio.
- What's arctan(1)?
- arctan(1) = 45° = π/4 radians, because tan(45°) = 1. Other common values: arctan(0) = 0; arctan(√3) = 60° = π/3; arctan(1/√3) = 30° = π/6.
- What about very large or very small x?
- As x → +∞, arctan(x) → 90° (or π/2 radians). As x → -∞, arctan(x) → -90° (or -π/2). For x = 1×10¹⁵ the calculator returns essentially 90°. For x near zero, arctan(x) ≈ x (small-angle approximation) — useful in calculus and physics.
- Why does arctan return a negative angle for a negative x?
- Because tan is an odd function: tan(-θ) = -tan(θ). So arctan inherits that symmetry: arctan(-x) = -arctan(x). Negative input → negative output, mirrored across zero. arctan(-1) = -45°.
- How is arctan used in real life?
- Surveying (computing slope angles from rise/run), navigation (bearing calculations), CAD and graphics (rotation angles), physics (projectile angles, phase shifts in AC circuits), and electronics (impedance angles). Anywhere you have a ratio and need the angle that produced it.
- Does this round the answer?
- The display rounds to 8 significant digits for radians and 6 decimal places for degrees — enough for engineering and academic work. The underlying calculation uses double-precision floating point (about 15-17 significant digits), the same precision your scientific calculator uses.
- Why is the π fraction shown?
- Because many textbook answers and physics formulas expect the angle in π form (π/4, π/6, π/3) rather than a decimal. The π fraction line shows arctan(x) ÷ π so you can read off whether the answer is a clean multiple of π.
- Is this the same as the arctan button on my calculator?
- Yes — the underlying function is identical (the standard IEEE-754 atan). Calculator manufacturers wrap it differently: some show tan⁻¹, some show atan, some show arctan. Same math.
