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    Sin 81 Degrees

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

    What is sin 81°?

    Answer

    sin 81° ≈
    0.9877

    Angle in radians: 81° = 9π/20. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places. An exact form of sin 81° in square roots exists, but it is unwieldy — nested radicals.

    P(cos 81°, sin 81°) ≈ (0.1564, 0.9877)

    xyOP

    P(cos 81°, sin 81°) ≈ (0.1564, 0.9877)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.9877.

    All four functions of 81°
    FunctionExact valueDecimal
    sin 81°—≈ 0.9877
    cos 81°—≈ 0.1564
    tan 81°—≈ 6.3138
    cot 81°—≈ 0.1584

    See Also

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    https://calculat.io/en/number/trigonometry/sin--81Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--81">Sin 81 Degrees: Sine of 81° on the Unit Circle - Calculatio</a>Copy
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    Sin 81 Degrees: Sine of 81° on the Unit Circle. sin 81° ≈ 0.9877. The sine is the y-coordinate of the point at 81° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--81/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    78°≈ 0.9781
    79°≈ 0.9816
    80°≈ 0.9848
    81°≈ 0.9877
    82°≈ 0.9903
    83°≈ 0.9925
    84°≈ 0.9945
    Recalculate with different values ↑

    FAQ

    What is sin 81°?

    sin 81° ≈ 0.9877

    Is there an exact value of sin 81°?

    Yes: 81° 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 81° ≈ 0.9877.

    Why does a calculator show −0.6299 for sin 81?

    The calculator is in radian mode (RAD): it takes sin 81 as the sine of 81 radians, sin 81 rad ≈ −0.6299. Switch it to degrees (DEG): sin 81° ≈ 0.9877. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also