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    Cos 345 Degrees

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

    What is cos 345°?

    Answer

    cos 345° =
    (√6 + √2)/4 ≈ 0.9659

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

    ≈ — rounded to 4 decimal places.

    cos 345° = cos(360° − 15°) = cos 15° = (√6 + √2)/4

    P(cos 345°, sin 345°) = ((√6 + √2)/4, −(√6 − √2)/4)

    cos 15° = cos(45° − 30°) = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4

    xyOP

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

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.9659.

    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: cos 15° = (√6 + √2)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--345Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--345">Cos 345 Degrees: Cosine of 345° on the Unit Circle</a>Copy
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    Cos 345 Degrees: Cosine of 345° on the Unit Circle. cos 345° = (√6 + √2)/4 ≈ 0.9659. The cosine is the x-coordinate of the point at 345° on the unit circle; 345° reduces to 15°.
    https://calculat.io/en/number/trigonometry/cos--345/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    330°√3/2
    341°≈ 0.9455
    342°√(10 + 2√5)/4
    345°(√6 + √2)/4
    355°≈ 0.9962
    360°1
    390°√3/2
    Recalculate with different values ↑

    FAQ

    What is cos 345°?

    cos 345° = (√6 + √2)/4 ≈ 0.9659

    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 0.8391 for cos 345?

    The calculator is in radian mode (RAD): it takes cos 345 as the cosine of 345 radians, cos 345 rad ≈ 0.8391. Switch it to degrees (DEG): cos 345° = (√6 + √2)/4 ≈ 0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also