Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Cos 108 Degrees

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

    What is cos 108°?

    Answer

    cos 108° =
    −(√5 − 1)/4 ≈ −0.3090

    Angle in radians: 108° = 3π/5. The point of the angle is in quadrant II, where cosine is negative.

    ≈ — rounded to 4 decimal places.

    cos 108° = cos(180° − 72°) = −cos 72° = −(√5 − 1)/4

    P(cos 108°, sin 108°) = (−(√5 − 1)/4, √(10 + 2√5)/4)

    Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

    cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

    xyOP

    P(cos 108°, sin 108°) ≈ (−0.3090, 0.9511)

    Highlighted: the projection on the x-axis — cosine, x ≈ −0.3090.

    All four functions of 108°
    FunctionExact valueDecimal
    sin 108°√(10 + 2√5)/4≈ 0.9511
    cos 108°−(√5 − 1)/4≈ −0.3090
    tan 108°−√(5 + 2√5)≈ −3.0777
    cot 108°−√(25 − 10√5)/5≈ −0.3249

    Reference angle: cos 72° = (√5 − 1)/4

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/cos--108Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--108">Cos 108 Degrees: Cosine of 108° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Cos 108 Degrees: Cosine of 108° on the Unit Circle. cos 108° = −(√5 − 1)/4 ≈ −0.3090. The cosine is the x-coordinate of the point at 108° on the unit circle; 108° reduces to 72°.
    https://calculat.io/en/number/trigonometry/cos--108/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    101°≈ −0.1908
    105°−(√6 − √2)/4
    106°≈ −0.2756
    108°−(√5 − 1)/4
    110°≈ −0.3420
    120°−1/2
    125°≈ −0.5736
    Recalculate with different values ↑

    FAQ

    What is cos 108°?

    cos 108° = −(√5 − 1)/4 ≈ −0.3090

    How are sin 18° and cos 72° related?

    They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

    Why does a calculator show 0.3755 for cos 108?

    The calculator is in radian mode (RAD): it takes cos 108 as the cosine of 108 radians, cos 108 rad ≈ 0.3755. Switch it to degrees (DEG): cos 108° = −(√5 − 1)/4 ≈ −0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also