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    Cos 15 Degrees

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

    What is cos 15°?

    Answer

    cos 15° =
    (√6 + √2)/4 ≈ 0.9659

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

    ≈ — rounded to 4 decimal places.

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

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

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

    Cosine of nearby angles

    Anglecos
    12°≈ 0.9781
    13°≈ 0.9744
    14°≈ 0.9703
    15°(√6 + √2)/4
    16°≈ 0.9613
    17°≈ 0.9563
    18°√(10 + 2√5)/4
    Recalculate with different values ↑

    FAQ

    What is cos 15°?

    cos 15° = (√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 −0.7597 for cos 15?

    The calculator is in radian mode (RAD): it takes cos 15 as the cosine of 15 radians, cos 15 rad ≈ −0.7597. Switch it to degrees (DEG): cos 15° = (√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