Arctan of −4/5

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arctan(−4/5)?

Answer

arctan(−4/5) ≈
−38.6598° ≈ −0.6747 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.

−4/5 = −0.8.

arctan(−4/5) is the angle α in (−90°, 90°) with tan α = −4/5.

arctan(−4/5) = −arctan(4/5) ≈ −38.6598°

tan(−38.6598°) ≈ −0.8000

xyOPT

α = arctan(−4/5) ≈ −38.6598°

P ≈ (0.7809, −0.6247)

T(1, −4/5) is where line OP meets the line x = 1; highlighted: tan α = −4/5.

All four inverse functions of −4/5
FunctionDegreesRadians
arcsin(−4/5)≈ −53.1301°≈ −0.9273
arccos(−4/5)≈ 143.1301°≈ 2.4981
arctan(−4/5)≈ −38.6598°≈ −0.6747
arccot(−4/5)≈ 128.6598°≈ 2.2455

See Also

Recalculate with different values ↑

Arctangent of nearby values

xarctan x
−√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°
00° = 0

FAQ

What is arctan(−4/5)?

arctan(−4/5) ≈ −38.6598° ≈ −0.6747 rad

Why is arctan(−4/5) ≈ −38.6598°?

arctan is an odd function: arctan(−x) = −arctan x. So arctan(−4/5) = −arctan(4/5) ≈ −38.6598°, and this angle lies in the range (−90°, 90°).

Why does a calculator show −0.6747 for arctan(−4/5)?

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(−4/5) ≈ −0.6747 rad. In degrees (DEG) it is ≈ −38.6598°.

See Also