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    Sin 36 Degrees

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

    What is sin 36°?

    Answer

    sin 36° =
    √(10 − 2√5)/4 ≈ 0.5878

    Angle in radians: 36° = π/5. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places.

    P(cos 36°, sin 36°) = ((√5 + 1)/4, √(10 − 2√5)/4)

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

    sin 36° = √(1 − cos² 36°) = √(10 − 2√5)/4

    xyOP

    P(cos 36°, sin 36°) ≈ (0.8090, 0.5878)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.5878.

    All four functions of 36°
    FunctionExact valueDecimal
    sin 36°√(10 − 2√5)/4≈ 0.5878
    cos 36°(√5 + 1)/4≈ 0.8090
    tan 36°√(5 − 2√5)≈ 0.7265
    cot 36°√(25 + 10√5)/5≈ 1.3764

    See Also

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    https://calculat.io/en/number/trigonometry/sin--36Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--36">Sin 36 Degrees: Sine of 36° on the Unit Circle - Calculatio</a>Copy
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    Sin 36 Degrees: Sine of 36° on the Unit Circle. sin 36° = √(10 − 2√5)/4 ≈ 0.5878. The sine is the y-coordinate of the point at 36° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--36/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    33°≈ 0.5446
    34°≈ 0.5592
    35°≈ 0.5736
    36°√(10 − 2√5)/4
    37°≈ 0.6018
    38°≈ 0.6157
    39°≈ 0.6293
    Recalculate with different values ↑

    FAQ

    What is sin 36°?

    sin 36° = √(10 − 2√5)/4 ≈ 0.5878

    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 −0.9918 for sin 36?

    The calculator is in radian mode (RAD): it takes sin 36 as the sine of 36 radians, sin 36 rad ≈ −0.9918. Switch it to degrees (DEG): sin 36° = √(10 − 2√5)/4 ≈ 0.5878. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also