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    Sin 690 Degrees

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

    What is sin 690°?

    Answer

    sin 690° =
    −1/2 = −0.5

    Angle in radians: 690° = 23π/6. 690° = 360° + 330° — a full turn plus 330°, quadrant IV, where sine is negative.

    sin 690° = sin(690° − 360°) = sin 330°

    sin 330° = sin(360° − 30°) = −sin 30° = −1/2

    P(cos 690°, sin 690°) = (√3/2, −1/2)

    Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

    sin 30° = 1/2

    xyOP

    P(cos 690°, sin 690°) ≈ (0.8660, −0.5)

    Highlighted: the projection on the y-axis — sine, y = −0.5.

    +1 turn: the drawing shows 330°.

    All four functions of 690°
    FunctionExact valueDecimal
    sin 690°−1/2−0.5
    cos 690°√3/2≈ 0.8660
    tan 690°−√3/3≈ −0.5774
    cot 690°−√3≈ −1.7321

    Reference angle: sin 30° = 1/2

    See Also

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    https://calculat.io/en/number/trigonometry/sin--690Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--690">Sin 690 Degrees: Sine of 690° on the Unit Circle</a>Copy
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    Sin 690 Degrees: Sine of 690° on the Unit Circle. sin 690° = −1/2 = −0.5. The sine is the y-coordinate of the point at 690° on the unit circle; 690° reduces to 30°.
    https://calculat.io/en/number/trigonometry/sin--690/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    390°1/2
    400°≈ 0.6428
    450°1
    540°0
    570°−1/2
    690°−1/2
    720°0
    Recalculate with different values ↑

    FAQ

    What is sin 690°?

    sin 690° = −1/2 = −0.5

    How to remember sin 30°, sin 45° and sin 60°?

    Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: sin 690° = −1/2 = −0.5.

    Why does a calculator show −0.9129 for sin 690?

    The calculator is in radian mode (RAD): it takes sin 690 as the sine of 690 radians, sin 690 rad ≈ −0.9129. Switch it to degrees (DEG): sin 690° = −1/2 = −0.5. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also