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    Tan 159 Degrees

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

    What is tan 159°?

    Answer

    tan 159° ≈
    −0.3839

    Angle in radians: 159° = 53π/60. The point of the angle is in quadrant II, where tangent is negative.

    ≈ — rounded to 4 decimal places. An exact form of tan 159° in square roots exists, but it is unwieldy — nested radicals.

    tan 159° = tan(180° − 21°) = −tan 21° ≈ −0.3839

    tan 159° = sin 159° / cos 159° ≈ −0.3839

    xyOP

    P(cos 159°, sin 159°) ≈ (−0.9336, 0.3584)

    T(1, tan 159°) ≈ (1, −0.3839) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    All four functions of 159°
    FunctionExact valueDecimal
    sin 159°—≈ 0.3584
    cos 159°—≈ −0.9336
    tan 159°—≈ −0.3839
    cot 159°—≈ −2.6051

    Reference angle: tan 21° ≈ 0.3839

    See Also

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    https://calculat.io/en/number/trigonometry/tan--159Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--159">Tan 159 Degrees: Tangent of 159° on the Unit Circle</a>Copy
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    Tan 159 Degrees: Tangent of 159° on the Unit Circle. tan 159° ≈ −0.3839. The tangent is the ratio y/x of the point at 159° on the unit circle; 159° reduces to 21°.
    https://calculat.io/en/number/trigonometry/tan--159/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    144°−√(5 − 2√5)
    145°≈ −0.7002
    150°−√3/3
    159°≈ −0.3839
    160°≈ −0.3640
    162°−√(25 − 10√5)/5
    164°≈ −0.2867
    Recalculate with different values ↑

    FAQ

    What is tan 159°?

    tan 159° ≈ −0.3839

    Is there an exact value of tan 159°?

    Yes: 159° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: tan 159° ≈ −0.3839.

    Why does a calculator show −2.7432 for tan 159?

    The calculator is in radian mode (RAD): it takes tan 159 as the tangent of 159 radians, tan 159 rad ≈ −2.7432. Switch it to degrees (DEG): tan 159° ≈ −0.3839. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also