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    Sin 720 Degrees

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

    What is sin 720°?

    Answer

    sin 720° =
    0

    Angle in radians: 720° = 4π. 720° = 2 · 360° — two full turns: the point is on the x-axis, (1, 0).

    sin 720° = sin(720° − 2 · 360°) = sin 0°

    P(cos 720°, sin 720°) = (1, 0)

    xyOP

    P(cos 720°, sin 720°) = (1, 0)

    The point lies on the x-axis, so its projection on the y-axis is 0: sin 720° = 0.

    +2 turns: the drawing shows 0°.

    All four functions of 720°
    FunctionExact valueDecimal
    sin 720°00
    cos 720°11
    tan 720°00
    cot 720°undefined—

    Reference angle: sin 0° = 0

    See Also

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    https://calculat.io/en/number/trigonometry/sin--720Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--720">Sin 720 Degrees: Sine of 720° on the Unit Circle</a>Copy
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    Sin 720 Degrees: Sine of 720° on the Unit Circle. sin 720° = 0. The sine is the y-coordinate of the point at 720° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--720/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    390°1/2
    400°≈ 0.6428
    450°1
    540°0
    570°−1/2
    690°−1/2
    720°0
    Recalculate with different values ↑

    FAQ

    What is sin 720°?

    sin 720° = 0

    Why is sin 720° equal to 0?

    720° ends at the same point as 0°, (1, 0), and sine is its the y-coordinate, so sin 720° = 0.

    Why does a calculator show −0.5441 for sin 720?

    The calculator is in radian mode (RAD): it takes sin 720 as the sine of 720 radians, sin 720 rad ≈ −0.5441. Switch it to degrees (DEG): sin 720° = 0. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also