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    Cos 144 Degrees

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

    What is cos 144°?

    Answer

    cos 144° =
    −(√5 + 1)/4 ≈ −0.8090

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

    ≈ — rounded to 4 decimal places.

    cos 144° = cos(180° − 36°) = −cos 36° = −(√5 + 1)/4

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

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

    xyOP

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

    Highlighted: the projection on the x-axis — cosine, x ≈ −0.8090.

    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: cos 36° = (√5 + 1)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--144Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--144">Cos 144 Degrees: Cosine of 144° on the Unit Circle</a>Copy
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    Cos 144 Degrees: Cosine of 144° on the Unit Circle. cos 144° = −(√5 + 1)/4 ≈ −0.8090. The cosine is the x-coordinate of the point at 144° on the unit circle; 144° reduces to 36°.
    https://calculat.io/en/number/trigonometry/cos--144/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    135°−√2/2
    140°≈ −0.7660
    142°≈ −0.7880
    144°−(√5 + 1)/4
    145°≈ −0.8192
    150°−√3/2
    159°≈ −0.9336
    Recalculate with different values ↑

    FAQ

    What is cos 144°?

    cos 144° = −(√5 + 1)/4 ≈ −0.8090

    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 0.8711 for cos 144?

    The calculator is in radian mode (RAD): it takes cos 144 as the cosine of 144 radians, cos 144 rad ≈ 0.8711. Switch it to degrees (DEG): cos 144° = −(√5 + 1)/4 ≈ −0.8090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also