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    Sin 162 Degrees

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

    What is sin 162°?

    Answer

    sin 162° =
    (√5 − 1)/4 ≈ 0.3090

    Angle in radians: 162° = 9π/10. The point of the angle is in quadrant II, where sine is positive.

    ≈ — rounded to 4 decimal places.

    sin 162° = sin(180° − 18°) = sin 18° = (√5 − 1)/4

    P(cos 162°, sin 162°) = (−√(10 + 2√5)/4, (√5 − 1)/4)

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

    sin 18° = cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

    xyOP

    P(cos 162°, sin 162°) ≈ (−0.9511, 0.3090)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.3090.

    All four functions of 162°
    FunctionExact valueDecimal
    sin 162°(√5 − 1)/4≈ 0.3090
    cos 162°−√(10 + 2√5)/4≈ −0.9511
    tan 162°−√(25 − 10√5)/5≈ −0.3249
    cot 162°−√(5 + 2√5)≈ −3.0777

    Reference angle: sin 18° = (√5 − 1)/4

    See Also

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    https://calculat.io/en/number/trigonometry/sin--162Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--162">Sin 162 Degrees: Sine of 162° on the Unit Circle</a>Copy
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    Sin 162 Degrees: Sine of 162° on the Unit Circle. sin 162° = (√5 − 1)/4 ≈ 0.3090. The sine is the y-coordinate of the point at 162° on the unit circle; 162° reduces to 18°.
    https://calculat.io/en/number/trigonometry/sin--162/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    150°1/2
    159°≈ 0.3584
    160°≈ 0.3420
    162°(√5 − 1)/4
    164°≈ 0.2756
    165°(√6 − √2)/4
    167°≈ 0.2250
    Recalculate with different values ↑

    FAQ

    What is sin 162°?

    sin 162° = (√5 − 1)/4 ≈ 0.3090

    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 −0.9785 for sin 162?

    The calculator is in radian mode (RAD): it takes sin 162 as the sine of 162 radians, sin 162 rad ≈ −0.9785. Switch it to degrees (DEG): sin 162° = (√5 − 1)/4 ≈ 0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also