Arccos of 60

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccos(60)?

Answer

arccos 60
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 60 is outside — no angle has such a cosine.

If 60 is an angle in degrees, you need the direct function: cos 60° = 1/2.

An angle α with cos α = 60 would have to lie on the line x = 60, but that line passes to the right of the circle.

xyO

The line x = 60 passes to the right of the circle, beyond the drawing: they have no common point, so no angle α has cos α = 60.

All four inverse functions of 60
FunctionDegreesRadians
arcsin(60)does not exist—
arccos(60)does not exist—
arctan(60)≈ 89.0452°≈ 1.5541
arccot(60)≈ 0.9548°≈ 0.0167

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(60)?

arccos 60 does not exist

Why does arccos 60 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. 60 is outside: the line x = 60 does not meet the circle, and no angle has a cosine of 60. If 60 is an angle in degrees, you need the direct function: cos 60° = 1/2.

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 60 does not exist.

See Also