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    Sin 390 Degrees

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

    What is sin 390°?

    Answer

    sin 390° =
    1/2 = 0.5

    Angle in radians: 390° = 13π/6. 390° = 360° + 30° — a full turn plus 30°, quadrant I, where sine is positive.

    sin 390° = sin(390° − 360°) = sin 30°

    P(cos 390°, sin 390°) = (√3/2, 1/2)

    Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

    sin 30° = 1/2

    xyOP

    P(cos 390°, sin 390°) ≈ (0.8660, 0.5)

    Highlighted: the projection on the y-axis — sine, y = 0.5.

    +1 turn: the drawing shows 30°.

    All four functions of 390°
    FunctionExact valueDecimal
    sin 390°1/20.5
    cos 390°√3/2≈ 0.8660
    tan 390°√3/3≈ 0.5774
    cot 390°√3≈ 1.7321

    Reference angle: sin 30° = 1/2

    See Also

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    https://calculat.io/en/number/trigonometry/sin--390Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--390">Sin 390 Degrees: Sine of 390° on the Unit Circle</a>Copy
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    Sin 390 Degrees: Sine of 390° on the Unit Circle. sin 390° = 1/2 = 0.5. The sine is the y-coordinate of the point at 390° on the unit circle; 390° reduces to 30°.
    https://calculat.io/en/number/trigonometry/sin--390/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    345°−(√6 − √2)/4
    355°≈ −0.0872
    360°0
    390°1/2
    400°≈ 0.6428
    450°1
    540°0
    Recalculate with different values ↑

    FAQ

    What is sin 390°?

    sin 390° = 1/2 = 0.5

    How to remember sin 30°, sin 45° and sin 60°?

    Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: sin 390° = 1/2 = 0.5.

    Why does a calculator show 0.4282 for sin 390?

    The calculator is in radian mode (RAD): it takes sin 390 as the sine of 390 radians, sin 390 rad ≈ 0.4282. Switch it to degrees (DEG): sin 390° = 1/2 = 0.5. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also