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    Tan 78 Degrees

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

    What is tan 78°?

    Answer

    tan 78° ≈
    4.7046

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

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

    tan 78° = sin 78° / cos 78° ≈ 4.7046

    xyOP

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

    T(1, tan 78°) ≈ (1, 4.7046) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

    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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    https://calculat.io/en/number/trigonometry/tan--78Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--78">Tan 78 Degrees: Tangent of 78° on the Unit Circle</a>Copy
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    Tan 78 Degrees: Tangent of 78° on the Unit Circle. tan 78° ≈ 4.7046. The tangent is the ratio y/x of the point at 78° on the unit circle.
    https://calculat.io/en/number/trigonometry/tan--78/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    75°2 + √3
    76°≈ 4.0108
    77°≈ 4.3315
    78°≈ 4.7046
    79°≈ 5.1446
    80°≈ 5.6713
    81°≈ 6.3138
    Recalculate with different values ↑

    FAQ

    What is tan 78°?

    tan 78° ≈ 4.7046

    Is there an exact value of tan 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: tan 78° ≈ 4.7046.

    Why does a calculator show −0.5992 for tan 78?

    The calculator is in radian mode (RAD): it takes tan 78 as the tangent of 78 radians, tan 78 rad ≈ −0.5992. Switch it to degrees (DEG): tan 78° ≈ 4.7046. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also