Arccos of −4/5

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccos(−4/5)?

Answer

arccos(−4/5) ≈
143.1301° ≈ 2.4981 rad

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

≈ — the value is not a table one; rounded to 4 decimal places.

−4/5 = −0.8.

arccos(−4/5) is the angle α in [0°, 180°] with cos α = −4/5.

arccos(−4/5) = 180° − arccos(4/5) ≈ 180° − 36.8699° = 143.1301°

cos 143.1301° ≈ −0.8000

xyOP

α = arccos(−4/5) ≈ 143.1301°

P = (−0.8, 0.6)

P lies on the line x = −4/5 in the upper half of the circle, where sin α ≥ 0; highlighted: cos α = −4/5.

All four inverse functions of −4/5
FunctionDegreesRadians
arcsin(−4/5)≈ −53.1301°≈ −0.9273
arccos(−4/5)≈ 143.1301°≈ 2.4981
arctan(−4/5)≈ −38.6598°≈ −0.6747
arccot(−4/5)≈ 128.6598°≈ 2.2455

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(−4/5)?

arccos(−4/5) ≈ 143.1301° ≈ 2.4981 rad

Why is arccos(−4/5) ≈ 143.1301° and not −36.8699°?

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(−4/5) = 180° − arccos(4/5) ≈ 180° − 36.8699° = 143.1301°. The angle −36.8699° does not fit: cos(−α) = cos α, so its cosine is positive.

Why does a calculator show 2.4981 for arccos(−4/5)?

The calculator is in radian mode (RAD) and gives the angle in radians: arccos(−4/5) ≈ 2.4981 rad. In degrees (DEG) it is ≈ 143.1301°.

See Also