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    Sin 164 Degrees

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

    What is sin 164°?

    Answer

    sin 164° ≈
    0.2756

    Angle in radians: 164° = 41π/45. The point of the angle is in quadrant II, where sine is positive.

    ≈ — rounded to 4 decimal places. sin 164° can't be written with square roots: 164° is not a multiple of 3°.

    sin 164° = sin(180° − 16°) = sin 16° ≈ 0.2756

    P(cos 164°, sin 164°) ≈ (−0.9613, 0.2756)

    xyOP

    P(cos 164°, sin 164°) ≈ (−0.9613, 0.2756)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.2756.

    All four functions of 164°
    FunctionExact valueDecimal
    sin 164°—≈ 0.2756
    cos 164°—≈ −0.9613
    tan 164°—≈ −0.2867
    cot 164°—≈ −3.4874

    Reference angle: sin 16° ≈ 0.2756

    See Also

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    https://calculat.io/en/number/trigonometry/sin--164Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--164">Sin 164 Degrees: Sine of 164° on the Unit Circle</a>Copy
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    Sin 164 Degrees: Sine of 164° on the Unit Circle. sin 164° ≈ 0.2756. The sine is the y-coordinate of the point at 164° on the unit circle; 164° reduces to 16°.
    https://calculat.io/en/number/trigonometry/sin--164/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    159°≈ 0.3584
    160°≈ 0.3420
    162°(√5 − 1)/4
    164°≈ 0.2756
    165°(√6 − √2)/4
    167°≈ 0.2250
    175°≈ 0.0872
    Recalculate with different values ↑

    FAQ

    What is sin 164°?

    sin 164° ≈ 0.2756

    Why does sin 164° have no exact value?

    A trigonometric value of a whole number of degrees can be written with square roots only when the angle is a multiple of 3°. 164° is not, so no such exact form exists; the value is used as a decimal: sin 164° ≈ 0.2756.

    Why does a calculator show 0.5949 for sin 164?

    The calculator is in radian mode (RAD): it takes sin 164 as the sine of 164 radians, sin 164 rad ≈ 0.5949. Switch it to degrees (DEG): sin 164° ≈ 0.2756. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also