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    Sin 126 Degrees

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

    What is sin 126°?

    Answer

    sin 126° =
    (√5 + 1)/4 ≈ 0.8090

    Angle in radians: 126° = 7π/10. The point of the angle is in quadrant II, where sine is positive.

    ≈ — rounded to 4 decimal places.

    sin 126° = sin(180° − 54°) = sin 54° = (√5 + 1)/4

    P(cos 126°, sin 126°) = (−√(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 126°, sin 126°) ≈ (−0.5878, 0.8090)

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

    All four functions of 126°
    FunctionExact valueDecimal
    sin 126°(√5 + 1)/4≈ 0.8090
    cos 126°−√(10 − 2√5)/4≈ −0.5878
    tan 126°−√(25 + 10√5)/5≈ −1.3764
    cot 126°−√(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--126Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--126">Sin 126 Degrees: Sine of 126° on the Unit Circle</a>Copy
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    Sin 126 Degrees: Sine of 126° on the Unit Circle. sin 126° = (√5 + 1)/4 ≈ 0.8090. The sine is the y-coordinate of the point at 126° on the unit circle; 126° reduces to 54°.
    https://calculat.io/en/number/trigonometry/sin--126/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    110°≈ 0.9397
    120°√3/2
    125°≈ 0.8192
    126°(√5 + 1)/4
    127°≈ 0.7986
    130°≈ 0.7660
    134°≈ 0.7193
    Recalculate with different values ↑

    FAQ

    What is sin 126°?

    sin 126° = (√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 0.3300 for sin 126?

    The calculator is in radian mode (RAD): it takes sin 126 as the sine of 126 radians, sin 126 rad ≈ 0.3300. Switch it to degrees (DEG): sin 126° = (√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