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    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.

    xyO

    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

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    https://calculat.io/en/number/inverse-trigonometry/arcsin--3-2Copy
    <a href="https://calculat.io/en/number/inverse-trigonometry/arcsin--3-2">Arcsin of 3/2 (Inverse Sine) in Degrees and Radians</a>Copy
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    Arcsin of 3/2 (Inverse Sine) in Degrees and Radians. arcsin 3/2 does not exist: the sine of any angle lies between −1 and 1, and 3/2 is outside. What you may have meant — below.
    https://calculat.io/en/number/inverse-trigonometry/arcsin--3-2/generated.jpgCopy

    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
    Recalculate with different values ↑

    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