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    Cos 400 Degrees

    Sin, Cos, Tan, Cot of an Angle
    Function
    Angle (°)

    What is cos 400°?

    Answer

    cos 400° ≈
    0.7660

    Angle in radians: 400° = 20π/9. 400° = 360° + 40° — a full turn plus 40°, quadrant I, where cosine is positive.

    ≈ — rounded to 4 decimal places. cos 400° can't be written with square roots: 400° is not a multiple of 3°.

    cos 400° = cos(400° − 360°) = cos 40°

    P(cos 400°, sin 400°) ≈ (0.7660, 0.6428)

    xyOP

    P(cos 400°, sin 400°) ≈ (0.7660, 0.6428)

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.7660.

    +1 turn: the drawing shows 40°.

    All four functions of 400°
    FunctionExact valueDecimal
    sin 400°—≈ 0.6428
    cos 400°—≈ 0.7660
    tan 400°—≈ 0.8391
    cot 400°—≈ 1.1918

    Reference angle: cos 40° ≈ 0.7660

    See Also

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    https://calculat.io/en/number/trigonometry/cos--400Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--400">Cos 400 Degrees: Cosine of 400° on the Unit Circle</a>Copy
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    Cos 400 Degrees: Cosine of 400° on the Unit Circle. cos 400° ≈ 0.7660. The cosine is the x-coordinate of the point at 400° on the unit circle; 400° reduces to 40°.
    https://calculat.io/en/number/trigonometry/cos--400/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    355°≈ 0.9962
    360°1
    390°√3/2
    400°≈ 0.7660
    450°0
    540°−1
    570°−√3/2
    Recalculate with different values ↑

    FAQ

    What is cos 400°?

    cos 400° ≈ 0.7660

    Why does cos 400° have no exact value?

    A trigonometric value of a whole number of degrees can be written with square roots only when the angle is a multiple of 3°. 400° is not, so no such exact form exists; the value is used as a decimal: cos 400° ≈ 0.7660.

    Why does a calculator show −0.5253 for cos 400?

    The calculator is in radian mode (RAD): it takes cos 400 as the cosine of 400 radians, cos 400 rad ≈ −0.5253. Switch it to degrees (DEG): cos 400° ≈ 0.7660. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also