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    Arcsin of 2

    Arcsin, Arccos, Arctan, Arccot
    Function
    x

    What is arcsin(2)?

    Answer

    arcsin 2
    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 2 is outside — no angle has such a sine.

    If 2 is an angle in degrees, you need the direct function: sin 2° ≈ 0.0349.

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

    xyO

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

    All four inverse functions of 2
    FunctionDegreesRadians
    arcsin(2)does not exist—
    arccos(2)does not exist—
    arctan(2)≈ 63.4349°≈ 1.1071
    arccot(2)≈ 26.5651°≈ 0.4636

    See Also

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

    FAQ

    What is arcsin(2)?

    arcsin 2 does not exist

    Why does arcsin 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. 2 is outside: the line y = 2 does not meet the circle, and no angle has a sine of 2. If 2 is an angle in degrees, you need the direct function: sin 2° ≈ 0.0349.

    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 2 does not exist.