Arctan of −1
Arcsin, Arccos, Arctan, Arccot
What is arctan(−1)?
Answer
arctan(−1) =
−45° = −π/4
Range: arctan x is an angle strictly between −90° and 90°, so the answer is unique.
arctan(−1) is the angle α in (−90°, 90°) with tan α = −1.
arctan(−1) = −arctan(1) = −45°
tan(−45°) = −1 ✓
α = arctan(−1) = −45°
P(cos(−45°), sin(−45°)) = (√2/2, −√2/2)
T(1, −1) is where line OP meets the line x = 1; highlighted: tan α = −1.
| Function | Degrees | Radians |
|---|---|---|
| arcsin(−1) | −90° | −π/2 |
| arccos(−1) | 180° | π |
| arctan(−1) | −45° | −π/4 |
| arccot(−1) | 135° | 3π/4 |
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See Also
- Sin, Cos, Tan, Cot of an Angle - Exact value in square roots and the decimal, with reduction to an acute angle on the unit circle
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
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Arctangent of nearby values
| x | arctan x |
|---|---|
| −2 | ≈ −63.4349° |
| −√3 | −60° = −π/3 |
| −4/3 | ≈ −53.1301° |
| −1 | −45° = −π/4 |
| −4/5 | ≈ −38.6598° |
| −√3/3 | −30° = −π/6 |
| −0.3 | ≈ −16.6992° |