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    Cos 690 Degrees

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

    What is cos 690°?

    Answer

    cos 690° =
    √3/2 ≈ 0.8660

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

    ≈ — rounded to 4 decimal places.

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

    cos 330° = cos(360° − 30°) = cos 30° = √3/2

    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.

    cos 30° = √(1 − 1/4) = √3/2

    xyOP

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

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.8660.

    +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: cos 30° = √3/2

    See Also

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    https://calculat.io/en/number/trigonometry/cos--690Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--690">Cos 690 Degrees: Cosine of 690° on the Unit Circle</a>Copy
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    Cos 690 Degrees: Cosine of 690° on the Unit Circle. cos 690° = √3/2 ≈ 0.8660. The cosine is the x-coordinate of the point at 690° on the unit circle; 690° reduces to 30°.
    https://calculat.io/en/number/trigonometry/cos--690/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    390°√3/2
    400°≈ 0.7660
    450°0
    540°−1
    570°−√3/2
    690°√3/2
    720°1
    Recalculate with different values ↑

    FAQ

    What is cos 690°?

    cos 690° = √3/2 ≈ 0.8660

    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: cos 690° = √3/2 ≈ 0.8660.

    Why does a calculator show 0.4081 for cos 690?

    The calculator is in radian mode (RAD): it takes cos 690 as the cosine of 690 radians, cos 690 rad ≈ 0.4081. Switch it to degrees (DEG): cos 690° = √3/2 ≈ 0.8660. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also