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    Tan 345 Degrees

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

    What is tan 345°?

    Answer

    tan 345° =
    √3 − 2 ≈ −0.2679

    Angle in radians: 345° = 23π/12. The point of the angle is in quadrant IV, where tangent is negative.

    ≈ — rounded to 4 decimal places.

    tan 345° = tan(360° − 15°) = −tan 15° = √3 − 2

    tan 345° = sin 345° / cos 345° = (−(√6 − √2)/4) / ((√6 + √2)/4) = √3 − 2

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

    xyOP

    P(cos 345°, sin 345°) ≈ (0.9659, −0.2588)

    T(1, tan 345°) ≈ (1, −0.2679) — where line OP meets the line x = 1.

    All four functions of 345°
    FunctionExact valueDecimal
    sin 345°−(√6 − √2)/4≈ −0.2588
    cos 345°(√6 + √2)/4≈ 0.9659
    tan 345°√3 − 2≈ −0.2679
    cot 345°−2 − √3≈ −3.7321

    Reference angle: tan 15° = 2 − √3

    See Also

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    https://calculat.io/en/number/trigonometry/tan--345Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--345">Tan 345 Degrees: Tangent of 345° on the Unit Circle</a>Copy
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    Tan 345 Degrees: Tangent of 345° on the Unit Circle. tan 345° = √3 − 2 ≈ −0.2679. The tangent is the ratio y/x of the point at 345° on the unit circle; 345° reduces to 15°.
    https://calculat.io/en/number/trigonometry/tan--345/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    330°−√3/3
    341°≈ −0.3443
    342°−√(25 − 10√5)/5
    345°√3 − 2
    355°≈ −0.0875
    360°0
    390°√3/3
    Recalculate with different values ↑

    FAQ

    What is tan 345°?

    tan 345° = √3 − 2 ≈ −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 −0.6483 for tan 345?

    The calculator is in radian mode (RAD): it takes tan 345 as the tangent of 345 radians, tan 345 rad ≈ −0.6483. Switch it to degrees (DEG): tan 345° = √3 − 2 ≈ −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