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    Cos 342 Degrees

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

    What is cos 342°?

    Answer

    cos 342° =
    √(10 + 2√5)/4 ≈ 0.9511

    Angle in radians: 342° = 19π/10. The point of the angle is in quadrant IV, where cosine is positive.

    ≈ — rounded to 4 decimal places.

    cos 342° = cos(360° − 18°) = cos 18° = √(10 + 2√5)/4

    P(cos 342°, sin 342°) = (√(10 + 2√5)/4, −(√5 − 1)/4)

    Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

    cos 18° = √(1 − sin² 18°) = √(10 + 2√5)/4

    xyOP

    P(cos 342°, sin 342°) ≈ (0.9511, −0.3090)

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.9511.

    All four functions of 342°
    FunctionExact valueDecimal
    sin 342°−(√5 − 1)/4≈ −0.3090
    cos 342°√(10 + 2√5)/4≈ 0.9511
    tan 342°−√(25 − 10√5)/5≈ −0.3249
    cot 342°−√(5 + 2√5)≈ −3.0777

    Reference angle: cos 18° = √(10 + 2√5)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--342Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--342">Cos 342 Degrees: Cosine of 342° on the Unit Circle</a>Copy
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    Cos 342 Degrees: Cosine of 342° on the Unit Circle. cos 342° = √(10 + 2√5)/4 ≈ 0.9511. The cosine is the x-coordinate of the point at 342° on the unit circle; 342° reduces to 18°.
    https://calculat.io/en/number/trigonometry/cos--342/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    324°(√5 + 1)/4
    330°√3/2
    341°≈ 0.9455
    342°√(10 + 2√5)/4
    345°(√6 + √2)/4
    355°≈ 0.9962
    360°1
    Recalculate with different values ↑

    FAQ

    What is cos 342°?

    cos 342° = √(10 + 2√5)/4 ≈ 0.9511

    How are sin 18° and cos 72° related?

    They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

    Why does a calculator show −0.9075 for cos 342?

    The calculator is in radian mode (RAD): it takes cos 342 as the cosine of 342 radians, cos 342 rad ≈ −0.9075. Switch it to degrees (DEG): cos 342° = √(10 + 2√5)/4 ≈ 0.9511. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also