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    Tan 126 Degrees

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

    What is tan 126°?

    Answer

    tan 126° =
    −√(25 + 10√5)/5 ≈ −1.3764

    Angle in radians: 126° = 7π/10. The point of the angle is in quadrant II, where tangent is negative.

    ≈ — rounded to 4 decimal places.

    tan 126° = tan(180° − 54°) = −tan 54° = −√(25 + 10√5)/5

    tan 126° = sin 126° / cos 126° = ((√5 + 1)/4) / (−√(10 − 2√5)/4) = −√(25 + 10√5)/5

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

    tan 54° = cot 36° = cos 36° / sin 36° = √(25 + 10√5)/5

    xyOP

    P(cos 126°, sin 126°) ≈ (−0.5878, 0.8090)

    T(1, tan 126°) ≈ (1, −1.3764) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    All four functions of 126°
    FunctionExact valueDecimal
    sin 126°(√5 + 1)/4≈ 0.8090
    cos 126°−√(10 − 2√5)/4≈ −0.5878
    tan 126°−√(25 + 10√5)/5≈ −1.3764
    cot 126°−√(5 − 2√5)≈ −0.7265

    Reference angle: tan 54° = √(25 + 10√5)/5

    See Also

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    https://calculat.io/en/number/trigonometry/tan--126Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--126">Tan 126 Degrees: Tangent of 126° on the Unit Circle</a>Copy
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    Tan 126 Degrees: Tangent of 126° on the Unit Circle. tan 126° = −√(25 + 10√5)/5 ≈ −1.3764. The tangent is the ratio y/x of the point at 126° on the unit circle; 126° reduces to 54°.
    https://calculat.io/en/number/trigonometry/tan--126/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    110°≈ −2.7475
    120°−√3
    125°≈ −1.4281
    126°−√(25 + 10√5)/5
    127°≈ −1.3270
    130°≈ −1.1918
    134°≈ −1.0355
    Recalculate with different values ↑

    FAQ

    What is tan 126°?

    tan 126° = −√(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 0.3496 for tan 126?

    The calculator is in radian mode (RAD): it takes tan 126 as the tangent of 126 radians, tan 126 rad ≈ 0.3496. Switch it to degrees (DEG): tan 126° = −√(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