Arccos of −1

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccos(−1)?

Answer

arccos(−1) =
180° = π

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

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

arccos(−1) = 180° − arccos(1) = 180° − 0° = 180°

cos 180° = −1 ✓

xyOP

α = arccos(−1) = 180°

P(cos 180°, sin 180°) = (−1, 0)

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

All four inverse functions of −1
FunctionDegreesRadians
arcsin(−1)−90°−π/2
arccos(−1)180°π
arctan(−1)−45°−π/4
arccot(−1)135°3π/4

See Also

Recalculate with different values ↑

Arccosine of nearby values

xarccos x
−1180° = π
−√3/2150° = 5π/6
−4/5≈ 143.1301°
−√2/2135° = 3π/4
−1/2120° = 2π/3
−0.3≈ 107.4576°
090° = π/2

FAQ

What is arccos(−1)?

arccos(−1) = 180° = π

Why is arccos(−1) = 180°?

The range of arccos is from 0° to 180°: there are no negative angles in it. A negative x gives an angle greater than 90°: arccos(−1) = 180° − arccos(1) = 180° − 0° = 180°.

Why does a calculator show 3.1416 for arccos(−1)?

The calculator is in radian mode (RAD) and gives the angle in radians: arccos(−1) = π ≈ 3.1416 rad. In degrees (DEG) it is 180°.

See Also