Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Tan 150 Degrees

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

    What is tan 150°?

    Answer

    tan 150° =
    −√3/3 ≈ −0.5774

    Angle in radians: 150° = 5π/6. The point of the angle is in quadrant II, where tangent is negative.

    ≈ — rounded to 4 decimal places.

    tan 150° = tan(180° − 30°) = −tan 30° = −√3/3

    tan 150° = sin 150° / cos 150° = (1/2) / (−√3/2) = −√3/3

    Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

    tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3

    xyOP

    P(cos 150°, sin 150°) ≈ (−0.8660, 0.5)

    T(1, tan 150°) ≈ (1, −0.5774) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    All four functions of 150°
    FunctionExact valueDecimal
    sin 150°1/20.5
    cos 150°−√3/2≈ −0.8660
    tan 150°−√3/3≈ −0.5774
    cot 150°−√3≈ −1.7321

    Reference angle: tan 30° = √3/3

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/tan--150Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--150">Tan 150 Degrees: Tangent of 150° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Tan 150 Degrees: Tangent of 150° on the Unit Circle. tan 150° = −√3/3 ≈ −0.5774. The tangent is the ratio y/x of the point at 150° on the unit circle; 150° reduces to 30°.
    https://calculat.io/en/number/trigonometry/tan--150/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    142°≈ −0.7813
    144°−√(5 − 2√5)
    145°≈ −0.7002
    150°−√3/3
    159°≈ −0.3839
    160°≈ −0.3640
    162°−√(25 − 10√5)/5
    Recalculate with different values ↑

    FAQ

    What is tan 150°?

    tan 150° = −√3/3 ≈ −0.5774

    How to remember sin 30°, sin 45° and sin 60°?

    Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: tan 150° = −√3/3 ≈ −0.5774.

    Why does a calculator show −1.0223 for tan 150?

    The calculator is in radian mode (RAD): it takes tan 150 as the tangent of 150 radians, tan 150 rad ≈ −1.0223. Switch it to degrees (DEG): tan 150° = −√3/3 ≈ −0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also