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    Tan 195 Degrees

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

    What is tan 195°?

    Answer

    tan 195° =
    2 − √3 ≈ 0.2679

    Angle in radians: 195° = 13π/12. The point of the angle is in quadrant III, where tangent is positive.

    ≈ — rounded to 4 decimal places.

    tan 195° = tan(180° + 15°) = tan 15° = 2 − √3

    tan 195° = sin 195° / cos 195° = (−(√6 − √2)/4) / (−(√6 + √2)/4) = 2 − √3

    tan 15° = tan(45° − 30°) = (1 − √3/3) / (1 + √3/3) = 2 − √3

    xyOP

    P(cos 195°, sin 195°) ≈ (−0.9659, −0.2588)

    T(1, tan 195°) ≈ (1, 0.2679) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    All four functions of 195°
    FunctionExact valueDecimal
    sin 195°−(√6 − √2)/4≈ −0.2588
    cos 195°−(√6 + √2)/4≈ −0.9659
    tan 195°2 − √3≈ 0.2679
    cot 195°2 + √3≈ 3.7321

    Reference angle: tan 15° = 2 − √3

    See Also

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    https://calculat.io/en/number/trigonometry/tan--195Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--195">Tan 195 Degrees: Tangent of 195° on the Unit Circle</a>Copy
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    Tan 195 Degrees: Tangent of 195° on the Unit Circle. tan 195° = 2 − √3 ≈ 0.2679. The tangent is the ratio y/x of the point at 195° on the unit circle; 195° reduces to 15°.
    https://calculat.io/en/number/trigonometry/tan--195/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    175°≈ −0.0875
    179°≈ −0.0175
    180°0
    195°2 − √3
    198°√(25 − 10√5)/5
    200°≈ 0.3640
    210°√3/3
    Recalculate with different values ↑

    FAQ

    What is tan 195°?

    tan 195° = 2 − √3 ≈ 0.2679

    How are sin 15° and cos 75° related?

    They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

    Why does a calculator show 0.2249 for tan 195?

    The calculator is in radian mode (RAD): it takes tan 195 as the tangent of 195 radians, tan 195 rad ≈ 0.2249. Switch it to degrees (DEG): tan 195° = 2 − √3 ≈ 0.2679. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also