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    Sin 51 Degrees

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

    What is sin 51°?

    Answer

    sin 51° ≈
    0.7771

    Angle in radians: 51° = 17π/60. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places. An exact form of sin 51° in square roots exists, but it is unwieldy — nested radicals.

    P(cos 51°, sin 51°) ≈ (0.6293, 0.7771)

    xyOP

    P(cos 51°, sin 51°) ≈ (0.6293, 0.7771)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.7771.

    All four functions of 51°
    FunctionExact valueDecimal
    sin 51°—≈ 0.7771
    cos 51°—≈ 0.6293
    tan 51°—≈ 1.2349
    cot 51°—≈ 0.8098

    See Also

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    https://calculat.io/en/number/trigonometry/sin--51Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--51">Sin 51 Degrees: Sine of 51° on the Unit Circle - Calculatio</a>Copy
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    Sin 51 Degrees: Sine of 51° on the Unit Circle. sin 51° ≈ 0.7771. The sine is the y-coordinate of the point at 51° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--51/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    48°≈ 0.7431
    49°≈ 0.7547
    50°≈ 0.7660
    51°≈ 0.7771
    52°≈ 0.7880
    53°≈ 0.7986
    54°(√5 + 1)/4
    Recalculate with different values ↑

    FAQ

    What is sin 51°?

    sin 51° ≈ 0.7771

    Is there an exact value of sin 51°?

    Yes: 51° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: sin 51° ≈ 0.7771.

    Why does a calculator show 0.6702 for sin 51?

    The calculator is in radian mode (RAD): it takes sin 51 as the sine of 51 radians, sin 51 rad ≈ 0.6702. Switch it to degrees (DEG): sin 51° ≈ 0.7771. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also