Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Cos 255 Degrees

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

    What is cos 255°?

    Answer

    cos 255° =
    −(√6 − √2)/4 ≈ −0.2588

    Angle in radians: 255° = 17π/12. The point of the angle is in quadrant III, where cosine is negative.

    ≈ — rounded to 4 decimal places.

    cos 255° = cos(180° + 75°) = −cos 75° = −(√6 − √2)/4

    P(cos 255°, sin 255°) = (−(√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 255°, sin 255°) ≈ (−0.2588, −0.9659)

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

    All four functions of 255°
    FunctionExact valueDecimal
    sin 255°−(√6 + √2)/4≈ −0.9659
    cos 255°−(√6 − √2)/4≈ −0.2588
    tan 255°2 + √3≈ 3.7321
    cot 255°2 − √3≈ 0.2679

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

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/cos--255Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--255">Cos 255 Degrees: Cosine of 255° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Cos 255 Degrees: Cosine of 255° on the Unit Circle. cos 255° = −(√6 − √2)/4 ≈ −0.2588. The cosine is the x-coordinate of the point at 255° on the unit circle; 255° reduces to 75°.
    https://calculat.io/en/number/trigonometry/cos--255/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    234°−√(10 − 2√5)/4
    240°−1/2
    252°−(√5 − 1)/4
    255°−(√6 − √2)/4
    270°0
    285°(√6 − √2)/4
    288°(√5 − 1)/4
    Recalculate with different values ↑

    FAQ

    What is cos 255°?

    cos 255° = −(√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 −0.8623 for cos 255?

    The calculator is in radian mode (RAD): it takes cos 255 as the cosine of 255 radians, cos 255 rad ≈ −0.8623. Switch it to degrees (DEG): cos 255° = −(√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