Arccos of 1/2

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccos(1/2)?

Answer

arccos(1/2) =
60° = π/3

Range: arccos x is an angle from 0° to 180°, so the answer is unique.

1/2 = 0.5.

arccos(1/2) is the angle α in [0°, 180°] with cos α = 1/2.

cos 60° = 1/2 ✓

xyOP

α = arccos(1/2) = 60°

P(cos 60°, sin 60°) = (1/2, √3/2)

P lies on the line x = 1/2 in the upper half of the circle, where sin α ≥ 0; highlighted: cos α = 1/2.

All four inverse functions of 1/2
FunctionDegreesRadians
arcsin(1/2)30°π/6
arccos(1/2)60°π/3
arctan(1/2)≈ 26.5651°≈ 0.4636
arccot(1/2)≈ 63.4349°≈ 1.1071

See Also

Recalculate with different values ↑

Arccosine of nearby values

xarccos x
0.3≈ 72.5424°
1/3≈ 70.5288°
2/5≈ 66.4218°
1/260° = π/3
0.55≈ 56.6330°
4/7≈ 55.1501°
√3/3≈ 54.7356°

FAQ

What is arccos(1/2)?

arccos(1/2) = 60° = π/3

How to find arccos(1/2) from a table of cosines?

Look in the table for the angle α in [0°, 180°] with cos α = 1/2: it is 60°, or π/3 in radians.

Why does a calculator show 1.0472 for arccos(1/2)?

The calculator is in radian mode (RAD) and gives the angle in radians: arccos(1/2) = π/3 ≈ 1.0472 rad. In degrees (DEG) it is 60°.

See Also