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    Sin 15 Degrees

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

    What is sin 15°?

    Answer

    sin 15° =
    (√6 − √2)/4 ≈ 0.2588

    Angle in radians: 15° = π/12. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places.

    P(cos 15°, sin 15°) = ((√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 15°, sin 15°) ≈ (0.9659, 0.2588)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.2588.

    All four functions of 15°
    FunctionExact valueDecimal
    sin 15°(√6 − √2)/4≈ 0.2588
    cos 15°(√6 + √2)/4≈ 0.9659
    tan 15°2 − √3≈ 0.2679
    cot 15°2 + √3≈ 3.7321

    See Also

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

    Sine of nearby angles

    Anglesin
    12°≈ 0.2079
    13°≈ 0.2250
    14°≈ 0.2419
    15°(√6 − √2)/4
    16°≈ 0.2756
    17°≈ 0.2924
    18°(√5 − 1)/4
    Recalculate with different values ↑

    FAQ

    What is sin 15°?

    sin 15° = (√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 0.6503 for sin 15?

    The calculator is in radian mode (RAD): it takes sin 15 as the sine of 15 radians, sin 15 rad ≈ 0.6503. Switch it to degrees (DEG): sin 15° = (√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