Arctan of √3/3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arctan(√3/3)?

Answer

arctan(√3/3) =
30° = π/6

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

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

tan 30° = √3/3 ✓

xyOP

α = arctan(√3/3) = 30°

P(cos 30°, sin 30°) = (√3/2, 1/2)

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

All four inverse functions of √3/3
FunctionDegreesRadians
arcsin(√3/3)≈ 35.2644°≈ 0.6155
arccos(√3/3)≈ 54.7356°≈ 0.9553
arctan(√3/3)30°π/6
arccot(√3/3)60°π/3

See Also

Recalculate with different values ↑

Arctangent of nearby values

xarctan x
1/3≈ 18.4349°
2/5≈ 21.8014°
1/2≈ 26.5651°
√3/330° = π/6
3/5≈ 30.9638°
2/3≈ 33.6901°
0.7≈ 34.9920°

FAQ

What is arctan(√3/3)?

arctan(√3/3) = 30° = π/6

How to find arctan(√3/3) from a table of tangents?

Look in the table for the angle α in (−90°, 90°) with tan α = √3/3: it is 30°, or π/6 in radians.

Why does a calculator show 0.5236 for arctan(√3/3)?

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(√3/3) = π/6 ≈ 0.5236 rad. In degrees (DEG) it is 30°.

See Also