Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Sin 165 Degrees

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

    What is sin 165°?

    Answer

    sin 165° =
    (√6 − √2)/4 ≈ 0.2588

    Angle in radians: 165° = 11π/12. The point of the angle is in quadrant II, where sine is positive.

    ≈ — rounded to 4 decimal places.

    sin 165° = sin(180° − 15°) = sin 15° = (√6 − √2)/4

    P(cos 165°, sin 165°) = (−(√6 + √2)/4, (√6 − √2)/4)

    sin 15° = sin(45° − 30°) = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4

    xyOP

    P(cos 165°, sin 165°) ≈ (−0.9659, 0.2588)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.2588.

    All four functions of 165°
    FunctionExact valueDecimal
    sin 165°(√6 − √2)/4≈ 0.2588
    cos 165°−(√6 + √2)/4≈ −0.9659
    tan 165°√3 − 2≈ −0.2679
    cot 165°−2 − √3≈ −3.7321

    Reference angle: sin 15° = (√6 − √2)/4

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/sin--165Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--165">Sin 165 Degrees: Sine of 165° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Sin 165 Degrees: Sine of 165° on the Unit Circle. sin 165° = (√6 − √2)/4 ≈ 0.2588. The sine is the y-coordinate of the point at 165° on the unit circle; 165° reduces to 15°.
    https://calculat.io/en/number/trigonometry/sin--165/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    160°≈ 0.3420
    162°(√5 − 1)/4
    164°≈ 0.2756
    165°(√6 − √2)/4
    167°≈ 0.2250
    175°≈ 0.0872
    179°≈ 0.0175
    Recalculate with different values ↑

    FAQ

    What is sin 165°?

    sin 165° = (√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 0.9978 for sin 165?

    The calculator is in radian mode (RAD): it takes sin 165 as the sine of 165 radians, sin 165 rad ≈ 0.9978. Switch it to degrees (DEG): sin 165° = (√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