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    Sin 234 Degrees

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

    What is sin 234°?

    Answer

    sin 234° =
    −(√5 + 1)/4 ≈ −0.8090

    Angle in radians: 234° = 13π/10. The point of the angle is in quadrant III, where sine is negative.

    ≈ — rounded to 4 decimal places.

    sin 234° = sin(180° + 54°) = −sin 54° = −(√5 + 1)/4

    P(cos 234°, sin 234°) = (−√(10 − 2√5)/4, −(√5 + 1)/4)

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

    sin 54° = cos 36° = (√5 + 1)/4

    xyOP

    P(cos 234°, sin 234°) ≈ (−0.5878, −0.8090)

    Highlighted: the projection on the y-axis — sine, y ≈ −0.8090.

    All four functions of 234°
    FunctionExact valueDecimal
    sin 234°−(√5 + 1)/4≈ −0.8090
    cos 234°−√(10 − 2√5)/4≈ −0.5878
    tan 234°√(25 + 10√5)/5≈ 1.3764
    cot 234°√(5 − 2√5)≈ 0.7265

    Reference angle: sin 54° = (√5 + 1)/4

    See Also

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    https://calculat.io/en/number/trigonometry/sin--234Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--234">Sin 234 Degrees: Sine of 234° on the Unit Circle</a>Copy
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    Sin 234 Degrees: Sine of 234° on the Unit Circle. sin 234° = −(√5 + 1)/4 ≈ −0.8090. The sine is the y-coordinate of the point at 234° on the unit circle; 234° reduces to 54°.
    https://calculat.io/en/number/trigonometry/sin--234/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    216°−√(10 − 2√5)/4
    225°−√2/2
    227°≈ −0.7314
    234°−(√5 + 1)/4
    240°−√3/2
    252°−√(10 + 2√5)/4
    255°−(√6 + √2)/4
    Recalculate with different values ↑

    FAQ

    What is sin 234°?

    sin 234° = −(√5 + 1)/4 ≈ −0.8090

    How are sin 36° and cos 54° related?

    They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

    Why does a calculator show 0.9988 for sin 234?

    The calculator is in radian mode (RAD): it takes sin 234 as the sine of 234 radians, sin 234 rad ≈ 0.9988. Switch it to degrees (DEG): sin 234° = −(√5 + 1)/4 ≈ −0.8090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also