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    Cos 285 Degrees

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

    What is cos 285°?

    Answer

    cos 285° =
    (√6 − √2)/4 ≈ 0.2588

    Angle in radians: 285° = 19π/12. The point of the angle is in quadrant IV, where cosine is positive.

    ≈ — rounded to 4 decimal places.

    cos 285° = cos(360° − 75°) = cos 75° = (√6 − √2)/4

    P(cos 285°, sin 285°) = ((√6 − √2)/4, −(√6 + √2)/4)

    cos 75° = cos(45° + 30°) = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4

    xyOP

    P(cos 285°, sin 285°) ≈ (0.2588, −0.9659)

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.2588.

    All four functions of 285°
    FunctionExact valueDecimal
    sin 285°−(√6 + √2)/4≈ −0.9659
    cos 285°(√6 − √2)/4≈ 0.2588
    tan 285°−2 − √3≈ −3.7321
    cot 285°√3 − 2≈ −0.2679

    Reference angle: cos 75° = (√6 − √2)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--285Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--285">Cos 285 Degrees: Cosine of 285° on the Unit Circle</a>Copy
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    Cos 285 Degrees: Cosine of 285° on the Unit Circle. cos 285° = (√6 − √2)/4 ≈ 0.2588. The cosine is the x-coordinate of the point at 285° on the unit circle; 285° reduces to 75°.
    https://calculat.io/en/number/trigonometry/cos--285/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    252°−(√5 − 1)/4
    255°−(√6 − √2)/4
    270°0
    285°(√6 − √2)/4
    288°(√5 − 1)/4
    300°1/2
    306°√(10 − 2√5)/4
    Recalculate with different values ↑

    FAQ

    What is cos 285°?

    cos 285° = (√6 − √2)/4 ≈ 0.2588

    How are sin 15° and cos 75° related?

    They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

    Why does a calculator show −0.6333 for cos 285?

    The calculator is in radian mode (RAD): it takes cos 285 as the cosine of 285 radians, cos 285 rad ≈ −0.6333. Switch it to degrees (DEG): cos 285° = (√6 − √2)/4 ≈ 0.2588. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also