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    Sin 78 Degrees

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

    What is sin 78°?

    Answer

    sin 78° ≈
    0.9781

    Angle in radians: 78° = 13π/30. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places. An exact form of sin 78° in square roots exists, but it is unwieldy — nested radicals.

    P(cos 78°, sin 78°) ≈ (0.2079, 0.9781)

    xyOP

    P(cos 78°, sin 78°) ≈ (0.2079, 0.9781)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.9781.

    All four functions of 78°
    FunctionExact valueDecimal
    sin 78°—≈ 0.9781
    cos 78°—≈ 0.2079
    tan 78°—≈ 4.7046
    cot 78°—≈ 0.2126

    See Also

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    <a href="https://calculat.io/en/number/trigonometry/sin--78">Sin 78 Degrees: Sine of 78° on the Unit Circle - Calculatio</a>Copy
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    Sin 78 Degrees: Sine of 78° on the Unit Circle. sin 78° ≈ 0.9781. The sine is the y-coordinate of the point at 78° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--78/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    75°(√6 + √2)/4
    76°≈ 0.9703
    77°≈ 0.9744
    78°≈ 0.9781
    79°≈ 0.9816
    80°≈ 0.9848
    81°≈ 0.9877
    Recalculate with different values ↑

    FAQ

    What is sin 78°?

    sin 78° ≈ 0.9781

    Is there an exact value of sin 78°?

    Yes: 78° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: sin 78° ≈ 0.9781.

    Why does a calculator show 0.5140 for sin 78?

    The calculator is in radian mode (RAD): it takes sin 78 as the sine of 78 radians, sin 78 rad ≈ 0.5140. Switch it to degrees (DEG): sin 78° ≈ 0.9781. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also