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    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

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    https://calculat.io/en/number/inverse-trigonometry/arcsin--4Copy
    <a href="https://calculat.io/en/number/inverse-trigonometry/arcsin--4">Arcsin of 4 (Inverse Sine) in Degrees and Radians</a>Copy
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    Arcsin of 4 (Inverse Sine) in Degrees and Radians. arcsin 4 does not exist: the sine of any angle lies between −1 and 1, and 4 is outside. What you may have meant — below.
    https://calculat.io/en/number/inverse-trigonometry/arcsin--4/generated.jpgCopy

    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.