Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Sin 285 Degrees

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

    What is sin 285°?

    Answer

    sin 285° =
    −(√6 + √2)/4 ≈ −0.9659

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

    ≈ — rounded to 4 decimal places.

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

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

    sin 75° = sin(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 y-axis — sine, y ≈ −0.9659.

    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: sin 75° = (√6 + √2)/4

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/sin--285Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--285">Sin 285 Degrees: Sine of 285° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Sin 285 Degrees: Sine of 285° on the Unit Circle. sin 285° = −(√6 + √2)/4 ≈ −0.9659. The sine is the y-coordinate of the point at 285° on the unit circle; 285° reduces to 75°.
    https://calculat.io/en/number/trigonometry/sin--285/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    252°−√(10 + 2√5)/4
    255°−(√6 + √2)/4
    270°−1
    285°−(√6 + √2)/4
    288°−√(10 + 2√5)/4
    300°−√3/2
    306°−(√5 + 1)/4
    Recalculate with different values ↑

    FAQ

    What is sin 285°?

    sin 285° = −(√6 + √2)/4 ≈ −0.9659

    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 0.7739 for sin 285?

    The calculator is in radian mode (RAD): it takes sin 285 as the sine of 285 radians, sin 285 rad ≈ 0.7739. Switch it to degrees (DEG): sin 285° = −(√6 + √2)/4 ≈ −0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also