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    Sin 345 Degrees

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

    What is sin 345°?

    Answer

    sin 345° =
    −(√6 − √2)/4 ≈ −0.2588

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

    ≈ — rounded to 4 decimal places.

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

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

    sin 15° = sin(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 y-axis — sine, y ≈ −0.2588.

    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: sin 15° = (√6 − √2)/4

    See Also

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    https://calculat.io/en/number/trigonometry/sin--345Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--345">Sin 345 Degrees: Sine of 345° on the Unit Circle</a>Copy
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    Sin 345 Degrees: Sine of 345° on the Unit Circle. sin 345° = −(√6 − √2)/4 ≈ −0.2588. The sine is the y-coordinate of the point at 345° on the unit circle; 345° reduces to 15°.
    https://calculat.io/en/number/trigonometry/sin--345/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    330°−1/2
    341°≈ −0.3256
    342°−(√5 − 1)/4
    345°−(√6 − √2)/4
    355°≈ −0.0872
    360°0
    390°1/2
    Recalculate with different values ↑

    FAQ

    What is sin 345°?

    sin 345° = −(√6 − √2)/4 ≈ −0.2588

    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 −0.5440 for sin 345?

    The calculator is in radian mode (RAD): it takes sin 345 as the sine of 345 radians, sin 345 rad ≈ −0.5440. Switch it to degrees (DEG): sin 345° = −(√6 − √2)/4 ≈ −0.2588. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also