Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Cos 165 Degrees

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

    What is cos 165°?

    Answer

    cos 165° =
    −(√6 + √2)/4 ≈ −0.9659

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

    ≈ — rounded to 4 decimal places.

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

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

    cos 15° = cos(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 x-axis — cosine, x ≈ −0.9659.

    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: cos 15° = (√6 + √2)/4

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/cos--165Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--165">Cos 165 Degrees: Cosine of 165° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Cos 165 Degrees: Cosine of 165° on the Unit Circle. cos 165° = −(√6 + √2)/4 ≈ −0.9659. The cosine is the x-coordinate of the point at 165° on the unit circle; 165° reduces to 15°.
    https://calculat.io/en/number/trigonometry/cos--165/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    160°≈ −0.9397
    162°−√(10 + 2√5)/4
    164°≈ −0.9613
    165°−(√6 + √2)/4
    167°≈ −0.9744
    175°≈ −0.9962
    179°≈ −0.9998
    Recalculate with different values ↑

    FAQ

    What is cos 165°?

    cos 165° = −(√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 −0.0663 for cos 165?

    The calculator is in radian mode (RAD): it takes cos 165 as the cosine of 165 radians, cos 165 rad ≈ −0.0663. Switch it to degrees (DEG): cos 165° = −(√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