Arctan of √3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arctan(√3)?

Answer

arctan(√3) =
60° = π/3

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

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

tan 60° = √3 ✓

xyOPT

α = arctan(√3) = 60°

P(cos 60°, sin 60°) = (1/2, √3/2)

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

All four inverse functions of √3
FunctionDegreesRadians
arcsin(√3)does not exist—
arccos(√3)does not exist—
arctan(√3)60°π/3
arccot(√3)30°π/6

See Also

Recalculate with different values ↑

Arctangent of nearby values

xarctan x
145° = π/4
3/2≈ 56.3099°
5/3≈ 59.0362°
√360° = π/3
2≈ 63.4349°
5/2≈ 68.1986°
3≈ 71.5651°

FAQ

What is arctan(√3)?

arctan(√3) = 60° = π/3

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

Look in the table for the angle α in (−90°, 90°) with tan α = √3: it is 60°, or π/3 in radians.

Why does a calculator show 1.0472 for arctan(√3)?

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(√3) = π/3 ≈ 1.0472 rad. In degrees (DEG) it is 60°.

See Also