Arcsin of −4/5

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arcsin(−4/5)?

Answer

arcsin(−4/5) ≈
−53.1301° ≈ −0.9273 rad

Range: arcsin x is an angle from −90° to 90°, so the answer is unique.

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

−4/5 = −0.8.

arcsin(−4/5) is the angle α in [−90°, 90°] with sin α = −4/5.

arcsin(−4/5) = −arcsin(4/5) ≈ −53.1301°

sin(−53.1301°) ≈ −0.8000

xyOP

α = arcsin(−4/5) ≈ −53.1301°

P = (0.6, −0.8)

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

Arcsine of nearby values

xarcsin x
−1−90° = −π/2
−√3/2−60° = −π/3
−4/5≈ −53.1301°
−√2/2−45° = −π/4
−1/2−30° = −π/6
−0.3≈ −17.4576°
00° = 0

FAQ

What is arcsin(−4/5)?

arcsin(−4/5) ≈ −53.1301° ≈ −0.9273 rad

Why is arcsin(−4/5) ≈ −53.1301°?

arcsin is an odd function: arcsin(−x) = −arcsin x. So arcsin(−4/5) = −arcsin(4/5) ≈ −53.1301°, and this angle lies in the range [−90°, 90°].

Why does a calculator show −0.9273 for arcsin(−4/5)?

The calculator is in radian mode (RAD) and gives the angle in radians: arcsin(−4/5) ≈ −0.9273 rad. In degrees (DEG) it is ≈ −53.1301°.

See Also