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    Tan 18 Degrees

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

    What is tan 18°?

    Answer

    tan 18° =
    √(25 − 10√5)/5 ≈ 0.3249

    Angle in radians: 18° = π/10. The point of the angle is in quadrant I, where tangent is positive.

    ≈ — rounded to 4 decimal places.

    tan 18° = sin 18° / cos 18° = ((√5 − 1)/4) / (√(10 + 2√5)/4) = √(25 − 10√5)/5

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

    tan 18° = sin 18° / cos 18° = √(25 − 10√5)/5

    xyOP

    P(cos 18°, sin 18°) ≈ (0.9511, 0.3090)

    T(1, tan 18°) ≈ (1, 0.3249) — where line OP meets the line x = 1.

    All four functions of 18°
    FunctionExact valueDecimal
    sin 18°(√5 − 1)/4≈ 0.3090
    cos 18°√(10 + 2√5)/4≈ 0.9511
    tan 18°√(25 − 10√5)/5≈ 0.3249
    cot 18°√(5 + 2√5)≈ 3.0777

    See Also

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    https://calculat.io/en/number/trigonometry/tan--18Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--18">Tan 18 Degrees: Tangent of 18° on the Unit Circle</a>Copy
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    Tan 18 Degrees: Tangent of 18° on the Unit Circle. tan 18° = √(25 − 10√5)/5 ≈ 0.3249. The tangent is the ratio y/x of the point at 18° on the unit circle.
    https://calculat.io/en/number/trigonometry/tan--18/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    15°2 − √3
    16°≈ 0.2867
    17°≈ 0.3057
    18°√(25 − 10√5)/5
    19°≈ 0.3443
    20°≈ 0.3640
    21°≈ 0.3839
    Recalculate with different values ↑

    FAQ

    What is tan 18°?

    tan 18° = √(25 − 10√5)/5 ≈ 0.3249

    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 −1.1373 for tan 18?

    The calculator is in radian mode (RAD): it takes tan 18 as the tangent of 18 radians, tan 18 rad ≈ −1.1373. Switch it to degrees (DEG): tan 18° = √(25 − 10√5)/5 ≈ 0.3249. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also