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    Arccos of −4/5

    Arcsin, Arccos, Arctan, Arccot
    Function
    x

    What is arccos(−4/5)?

    Answer

    arccos(−4/5) ≈
    143.1301° ≈ 2.4981 rad

    Range: arccos x is an angle from 0° to 180°, so the answer is unique.

    ≈ — the value is not a table one; rounded to 4 decimal places.

    −4/5 = −0.8.

    arccos(−4/5) is the angle α in [0°, 180°] with cos α = −4/5.

    arccos(−4/5) = 180° − arccos(4/5) ≈ 180° − 36.8699° = 143.1301°

    cos 143.1301° ≈ −0.8000

    xyOP

    α = arccos(−4/5) ≈ 143.1301°

    P = (−0.8, 0.6)

    P lies on the line x = −4/5 in the upper half of the circle, where sin α ≥ 0; highlighted: cos α = −4/5.

    All four inverse functions of −4/5
    FunctionDegreesRadians
    arcsin(−4/5)≈ −53.1301°≈ −0.9273
    arccos(−4/5)≈ 143.1301°≈ 2.4981
    arctan(−4/5)≈ −38.6598°≈ −0.6747
    arccot(−4/5)≈ 128.6598°≈ 2.2455

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    https://calculat.io/en/number/inverse-trigonometry/arccos---4-5Copy
    <a href="https://calculat.io/en/number/inverse-trigonometry/arccos---4-5">Arccos of −4/5 (Inverse Cosine) in Degrees and Radians</a>Copy
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    Arccos of −4/5 (Inverse Cosine) in Degrees and Radians. arccos(−4/5) ≈ 143.1301° ≈ 2.4981 rad: the angle in [0°, 180°] whose cosine is −4/5. With the check and the unit circle.
    https://calculat.io/en/number/inverse-trigonometry/arccos---4-5/generated.jpgCopy

    FAQ

    What is arccos(−4/5)?

    arccos(−4/5) ≈ 143.1301° ≈ 2.4981 rad

    Why is arccos(−4/5) ≈ 143.1301° and not −36.8699°?

    The range of arccos is from 0° to 180°: there are no negative angles in it. A negative x gives an angle greater than 90°: arccos(−4/5) = 180° − arccos(4/5) ≈ 180° − 36.8699° = 143.1301°. The angle −36.8699° does not fit: cos(−α) = cos α, so its cosine is positive.

    Why does a calculator show 2.4981 for arccos(−4/5)?

    The calculator is in radian mode (RAD) and gives the angle in radians: arccos(−4/5) ≈ 2.4981 rad. In degrees (DEG) it is ≈ 143.1301°.