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    Sin 66 Degrees

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

    What is sin 66°?

    Answer

    sin 66° ≈
    0.9135

    Angle in radians: 66° = 11π/30. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places. An exact form of sin 66° in square roots exists, but it is unwieldy — nested radicals.

    P(cos 66°, sin 66°) ≈ (0.4067, 0.9135)

    xyOP

    P(cos 66°, sin 66°) ≈ (0.4067, 0.9135)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.9135.

    All four functions of 66°
    FunctionExact valueDecimal
    sin 66°—≈ 0.9135
    cos 66°—≈ 0.4067
    tan 66°—≈ 2.2460
    cot 66°—≈ 0.4452

    See Also

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    <a href="https://calculat.io/en/number/trigonometry/sin--66">Sin 66 Degrees: Sine of 66° on the Unit Circle - Calculatio</a>Copy
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    Sin 66 Degrees: Sine of 66° on the Unit Circle. sin 66° ≈ 0.9135. The sine is the y-coordinate of the point at 66° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--66/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    63°≈ 0.8910
    64°≈ 0.8988
    65°≈ 0.9063
    66°≈ 0.9135
    67°≈ 0.9205
    68°≈ 0.9272
    69°≈ 0.9336
    Recalculate with different values ↑

    FAQ

    What is sin 66°?

    sin 66° ≈ 0.9135

    Is there an exact value of sin 66°?

    Yes: 66° 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 66° ≈ 0.9135.

    Why does a calculator show −0.0266 for sin 66?

    The calculator is in radian mode (RAD): it takes sin 66 as the sine of 66 radians, sin 66 rad ≈ −0.0266. Switch it to degrees (DEG): sin 66° ≈ 0.9135. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also