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    Sin 400 Degrees

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

    What is sin 400°?

    Answer

    sin 400° ≈
    0.6428

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

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

    sin 400° = sin(400° − 360°) = sin 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 y-axis — sine, y ≈ 0.6428.

    +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: sin 40° ≈ 0.6428

    See Also

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    https://calculat.io/en/number/trigonometry/sin--400Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--400">Sin 400 Degrees: Sine of 400° on the Unit Circle</a>Copy
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    Sin 400 Degrees: Sine of 400° on the Unit Circle. sin 400° ≈ 0.6428. The sine is the y-coordinate of the point at 400° on the unit circle; 400° reduces to 40°.
    https://calculat.io/en/number/trigonometry/sin--400/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    355°≈ −0.0872
    360°0
    390°1/2
    400°≈ 0.6428
    450°1
    540°0
    570°−1/2
    Recalculate with different values ↑

    FAQ

    What is sin 400°?

    sin 400° ≈ 0.6428

    Why does sin 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: sin 400° ≈ 0.6428.

    Why does a calculator show −0.8509 for sin 400?

    The calculator is in radian mode (RAD): it takes sin 400 as the sine of 400 radians, sin 400 rad ≈ −0.8509. Switch it to degrees (DEG): sin 400° ≈ 0.6428. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also