Arcsin of 4

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arcsin(4)?

Answer

arcsin 4
does not exist

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

The sine of any angle lies between −1 and 1, and 4 is outside — no angle has such a sine.

If 4 is an angle in degrees, you need the direct function: sin 4° ≈ 0.0698.

An angle α with sin α = 4 would have to lie on the line y = 4, but that line passes above the circle.

xyO

The line y = 4 passes above the circle, beyond the drawing: they have no common point, so no angle α has sin α = 4.

All four inverse functions of 4
FunctionDegreesRadians
arcsin(4)does not exist—
arccos(4)does not exist—
arctan(4)≈ 75.9638°≈ 1.3258
arccot(4)≈ 14.0362°≈ 0.2450

See Also

Recalculate with different values ↑

Arcsine of nearby values

xarcsin x
4/5≈ 53.1301°
√3/260° = π/3
0.9≈ 64.1581°
190° = π/2
3/2does not exist
2does not exist
4does not exist

FAQ

What is arcsin(4)?

arcsin 4 does not exist

Why does arcsin 4 not exist?

The sine is the y-coordinate of a point on the unit circle, so the sine of any angle lies between −1 and 1. 4 is outside: the line y = 4 does not meet the circle, and no angle has a sine of 4. If 4 is an angle in degrees, you need the direct function: sin 4° ≈ 0.0698.

What is the difference between arcsin, sin⁻¹ and 1/sin?

sin⁻¹ x is another way to write arcsin x (that is how the calculator key is labelled), not 1/sin x: 1/sin x is the cosecant. arcsin x is the angle whose sine is x; it exists only for −1 ≤ x ≤ 1. Here: arcsin 4 does not exist.

See Also