Arctan of −3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arctan(−3)?

Answer

arctan(−3) ≈
−71.5651° ≈ −1.2490 rad

Range: arctan x is an angle strictly between −90° and 90°, so the answer is unique.

≈ — the value is not a table one; rounded to 4 decimal places.

arctan(−3) is the angle α in (−90°, 90°) with tan α = −3.

arctan(−3) = −arctan(3) ≈ −71.5651°

tan(−71.5651°) ≈ −3.0000

xyOP

α = arctan(−3) ≈ −71.5651°

P ≈ (0.3162, −0.9487)

T(1, −3) is where line OP meets the line x = 1, beyond the drawing (the arrow points to it); highlighted: tan α = −3.

All four inverse functions of −3
FunctionDegreesRadians
arcsin(−3)does not exist—
arccos(−3)does not exist—
arctan(−3)≈ −71.5651°≈ −1.2490
arccot(−3)≈ 161.5651°≈ 2.8198

See Also

Recalculate with different values ↑

Arctangent of nearby values

xarctan x
−3≈ −71.5651°
−2≈ −63.4349°
−√3−60° = −π/3
−4/3≈ −53.1301°
−1−45° = −π/4
−4/5≈ −38.6598°
−√3/3−30° = −π/6

FAQ

What is arctan(−3)?

arctan(−3) ≈ −71.5651° ≈ −1.2490 rad

Why is arctan(−3) ≈ −71.5651°?

arctan is an odd function: arctan(−x) = −arctan x. So arctan(−3) = −arctan(3) ≈ −71.5651°, and this angle lies in the range (−90°, 90°).

Why does a calculator show −1.2490 for arctan(−3)?

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(−3) ≈ −1.2490 rad. In degrees (DEG) it is ≈ −71.5651°.

See Also