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    Cot 345 Degrees

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

    What is cot 345°?

    Answer

    cot 345° =
    −2 − √3 ≈ −3.7321

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

    ≈ — rounded to 4 decimal places.

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

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

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

    xyOP

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

    C(cot 345°, 1) ≈ (−3.7321, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed); C is beyond the drawing, the arrow points to it.

    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: cot 15° = 2 + √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--345Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--345">Cot 345 Degrees: Cotangent of 345° on the Unit Circle</a>Copy
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    Cot 345 Degrees: Cotangent of 345° on the Unit Circle. cot 345° = −2 − √3 ≈ −3.7321. The cotangent is the ratio x/y of the point at 345° on the unit circle; 345° reduces to 15°.
    https://calculat.io/en/number/trigonometry/cot--345/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    330°−√3
    341°≈ −2.9042
    342°−√(5 + 2√5)
    345°−2 − √3
    355°≈ −11.4301
    360°undefined
    390°√3
    Recalculate with different values ↑

    FAQ

    What is cot 345°?

    cot 345° = −2 − √3 ≈ −3.7321

    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 −1.5425 for cot 345?

    The calculator is in radian mode (RAD): it takes cot 345 as the cotangent of 345 radians, cot 345 rad ≈ −1.5425. Switch it to degrees (DEG): cot 345° = −2 − √3 ≈ −3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also