Arcsin of 3/2

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arcsin(3/2)?

Answer

arcsin 3/2
does not exist

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

3/2 = 1.5.

The sine of any angle lies between −1 and 1, and 3/2 is outside — no angle has such a sine.

If you meant √3/2: arcsin(√3/2) = 60°.

An angle α with sin α = 3/2 would have to lie on the line y = 3/2, but that line passes above the circle.

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The line y = 3/2 passes above the circle: they have no common point, so no angle α has sin α = 3/2.

All four inverse functions of 3/2
FunctionDegreesRadians
arcsin(3/2)does not exist—
arccos(3/2)does not exist—
arctan(3/2)≈ 56.3099°≈ 0.9828
arccot(3/2)≈ 33.6901°≈ 0.5880

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(3/2)?

arcsin 3/2 does not exist

Why does arcsin 3/2 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. 3/2 is outside: the line y = 3/2 does not meet the circle, and no angle has a sine of 3/2. If you meant √3/2: arcsin(√3/2) = 60°.

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 3/2 does not exist.

See Also