Arctan of −4/3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arctan(−4/3)?

Answer

arctan(−4/3) ≈
−53.1301° ≈ −0.9273 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(−4/3) is the angle α in (−90°, 90°) with tan α = −4/3.

arctan(−4/3) = −arctan(4/3) ≈ −53.1301°

tan(−53.1301°) ≈ −1.3333

xyOPT

α = arctan(−4/3) ≈ −53.1301°

P = (0.6, −0.8)

T(1, −4/3) is where line OP meets the line x = 1; highlighted: tan α = −4/3.

All four inverse functions of −4/3
FunctionDegreesRadians
arcsin(−4/3)does not exist—
arccos(−4/3)does not exist—
arctan(−4/3)≈ −53.1301°≈ −0.9273
arccot(−4/3)≈ 143.1301°≈ 2.4981

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(−4/3)?

arctan(−4/3) ≈ −53.1301° ≈ −0.9273 rad

Why is arctan(−4/3) ≈ −53.1301°?

arctan is an odd function: arctan(−x) = −arctan x. So arctan(−4/3) = −arctan(4/3) ≈ −53.1301°, and this angle lies in the range (−90°, 90°).

Why does a calculator show −0.9273 for arctan(−4/3)?

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(−4/3) ≈ −0.9273 rad. In degrees (DEG) it is ≈ −53.1301°.

See Also