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    Sin 40 Degrees

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

    What is sin 40°?

    Answer

    sin 40° ≈
    0.6428

    Angle in radians: 40° = 2π/9. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places. sin 40° can't be written with square roots: 40° is not a multiple of 3°.

    P(cos 40°, sin 40°) ≈ (0.7660, 0.6428)

    xyOP

    P(cos 40°, sin 40°) ≈ (0.7660, 0.6428)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.6428.

    All four functions of 40°
    FunctionExact valueDecimal
    sin 40°—≈ 0.6428
    cos 40°—≈ 0.7660
    tan 40°—≈ 0.8391
    cot 40°—≈ 1.1918

    See Also

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

    Sine of nearby angles

    Anglesin
    37°≈ 0.6018
    38°≈ 0.6157
    39°≈ 0.6293
    40°≈ 0.6428
    41°≈ 0.6561
    42°≈ 0.6691
    43°≈ 0.6820
    Recalculate with different values ↑

    FAQ

    What is sin 40°?

    sin 40° ≈ 0.6428

    Why does sin 40° 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°. 40° is not, so no such exact form exists; the value is used as a decimal: sin 40° ≈ 0.6428.

    Why does a calculator show 0.7451 for sin 40?

    The calculator is in radian mode (RAD): it takes sin 40 as the sine of 40 radians, sin 40 rad ≈ 0.7451. Switch it to degrees (DEG): sin 40° ≈ 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