Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Cot 144 Degrees

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

    What is cot 144°?

    Answer

    cot 144° =
    −√(25 + 10√5)/5 ≈ −1.3764

    Angle in radians: 144° = 4π/5. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 144° = cot(180° − 36°) = −cot 36° = −√(25 + 10√5)/5

    cot 144° = cos 144° / sin 144° = (−(√5 + 1)/4) / (√(10 − 2√5)/4) = −√(25 + 10√5)/5

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

    cot 36° = cos 36° / sin 36° = √(25 + 10√5)/5

    xyOP

    P(cos 144°, sin 144°) ≈ (−0.8090, 0.5878)

    C(cot 144°, 1) ≈ (−1.3764, 1) — where line OP meets the line y = 1.

    All four functions of 144°
    FunctionExact valueDecimal
    sin 144°√(10 − 2√5)/4≈ 0.5878
    cos 144°−(√5 + 1)/4≈ −0.8090
    tan 144°−√(5 − 2√5)≈ −0.7265
    cot 144°−√(25 + 10√5)/5≈ −1.3764

    Reference angle: cot 36° = √(25 + 10√5)/5

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/cot--144Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--144">Cot 144 Degrees: Cotangent of 144° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Cot 144 Degrees: Cotangent of 144° on the Unit Circle. cot 144° = −√(25 + 10√5)/5 ≈ −1.3764. The cotangent is the ratio x/y of the point at 144° on the unit circle; 144° reduces to 36°.
    https://calculat.io/en/number/trigonometry/cot--144/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    135°−1
    140°≈ −1.1918
    142°≈ −1.2799
    144°−√(25 + 10√5)/5
    145°≈ −1.4281
    150°−√3
    159°≈ −2.6051
    Recalculate with different values ↑

    FAQ

    What is cot 144°?

    cot 144° = −√(25 + 10√5)/5 ≈ −1.3764

    How are sin 36° and cos 54° related?

    They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

    Why does a calculator show −1.7742 for cot 144?

    The calculator is in radian mode (RAD): it takes cot 144 as the cotangent of 144 radians, cot 144 rad ≈ −1.7742. Switch it to degrees (DEG): cot 144° = −√(25 + 10√5)/5 ≈ −1.3764. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also