Arccos of 1

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccos(1)?

Answer

arccos(1) =
0° = 0

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.

cos 0° = 1 ✓

xyOP

α = arccos(1) = 0°

P(cos 0°, sin 0°) = (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)0°0
arctan(1)45°π/4
arccot(1)45°π/4

See Also

Recalculate with different values ↑

Arccosine of nearby values

xarccos x
4/5≈ 36.8699°
√3/230° = π/6
0.9≈ 25.8419°
12/13≈ 22.6199°
10° = 0
2does not exist
60does not exist

FAQ

What is arccos(1)?

arccos(1) = 0° = 0

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

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

What is the difference between arccos, cos⁻¹ and 1/cos?

cos⁻¹ x is another way to write arccos x (that is how the calculator key is labelled), not 1/cos x: 1/cos x is the secant. arccos x is the angle whose cosine is x; it exists only for −1 ≤ x ≤ 1. Here: arccos(1) = 0° = 0.

See Also