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    Tan 81 Degrees

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

    What is tan 81°?

    Answer

    tan 81° ≈
    6.3138

    Angle in radians: 81° = 9π/20. The point of the angle is in quadrant I, where tangent is positive.

    ≈ — rounded to 4 decimal places. An exact form of tan 81° in square roots exists, but it is unwieldy — nested radicals.

    tan 81° = sin 81° / cos 81° ≈ 6.3138

    xyOP

    P(cos 81°, sin 81°) ≈ (0.1564, 0.9877)

    T(1, tan 81°) ≈ (1, 6.3138) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

    All four functions of 81°
    FunctionExact valueDecimal
    sin 81°—≈ 0.9877
    cos 81°—≈ 0.1564
    tan 81°—≈ 6.3138
    cot 81°—≈ 0.1584

    See Also

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    https://calculat.io/en/number/trigonometry/tan--81Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--81">Tan 81 Degrees: Tangent of 81° on the Unit Circle</a>Copy
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    Tan 81 Degrees: Tangent of 81° on the Unit Circle. tan 81° ≈ 6.3138. The tangent is the ratio y/x of the point at 81° on the unit circle.
    https://calculat.io/en/number/trigonometry/tan--81/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    78°≈ 4.7046
    79°≈ 5.1446
    80°≈ 5.6713
    81°≈ 6.3138
    82°≈ 7.1154
    83°≈ 8.1443
    84°≈ 9.5144
    Recalculate with different values ↑

    FAQ

    What is tan 81°?

    tan 81° ≈ 6.3138

    Is there an exact value of tan 81°?

    Yes: 81° 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 81° ≈ 6.3138.

    Why does a calculator show −0.8110 for tan 81?

    The calculator is in radian mode (RAD): it takes tan 81 as the tangent of 81 radians, tan 81 rad ≈ −0.8110. Switch it to degrees (DEG): tan 81° ≈ 6.3138. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also