Arccos of 2

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccos(2)?

Answer

arccos 2
does not exist

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

The cosine of any angle lies between −1 and 1, and 2 is outside — no angle has such a cosine.

If 2 is an angle in degrees, you need the direct function: cos 2° ≈ 0.9994.

An angle α with cos α = 2 would have to lie on the line x = 2, but that line passes to the right of the circle.

xyO

The line x = 2 passes to the right of the circle: they have no common point, so no angle α has cos α = 2.

All four inverse functions of 2
FunctionDegreesRadians
arcsin(2)does not exist—
arccos(2)does not exist—
arctan(2)≈ 63.4349°≈ 1.1071
arccot(2)≈ 26.5651°≈ 0.4636

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(2)?

arccos 2 does not exist

Why does arccos 2 not exist?

The cosine is the x-coordinate of a point on the unit circle, so the cosine of any angle lies between −1 and 1. 2 is outside: the line x = 2 does not meet the circle, and no angle has a cosine of 2. If 2 is an angle in degrees, you need the direct function: cos 2° ≈ 0.9994.

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 2 does not exist.

See Also