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    Tan 100 Degrees

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

    What is tan 100°?

    Answer

    tan 100° ≈
    −5.6713

    Angle in radians: 100° = 5π/9. The point of the angle is in quadrant II, where tangent is negative.

    ≈ — rounded to 4 decimal places. tan 100° can't be written with square roots: 100° is not a multiple of 3°.

    tan 100° = tan(180° − 80°) = −tan 80° ≈ −5.6713

    tan 100° = sin 100° / cos 100° ≈ −5.6713

    xyOP

    P(cos 100°, sin 100°) ≈ (−0.1736, 0.9848)

    T(1, tan 100°) ≈ (1, −5.6713) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed); T is beyond the drawing, the arrow points to it.

    All four functions of 100°
    FunctionExact valueDecimal
    sin 100°—≈ 0.9848
    cos 100°—≈ −0.1736
    tan 100°—≈ −5.6713
    cot 100°—≈ −0.1763

    Reference angle: tan 80° ≈ 5.6713

    See Also

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    https://calculat.io/en/number/trigonometry/tan--100Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--100">Tan 100 Degrees: Tangent of 100° on the Unit Circle</a>Copy
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    Tan 100 Degrees: Tangent of 100° on the Unit Circle. tan 100° ≈ −5.6713. The tangent is the ratio y/x of the point at 100° on the unit circle; 100° reduces to 80°.
    https://calculat.io/en/number/trigonometry/tan--100/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    90°undefined
    97°≈ −8.1443
    98°≈ −7.1154
    100°≈ −5.6713
    101°≈ −5.1446
    105°−2 − √3
    106°≈ −3.4874
    Recalculate with different values ↑

    FAQ

    What is tan 100°?

    tan 100° ≈ −5.6713

    Why does tan 100° have no exact value?

    A trigonometric value of a whole number of degrees can be written with square roots only when the angle is a multiple of 3°. 100° is not, so no such exact form exists; the value is used as a decimal: tan 100° ≈ −5.6713.

    Why does a calculator show −0.5872 for tan 100?

    The calculator is in radian mode (RAD): it takes tan 100 as the tangent of 100 radians, tan 100 rad ≈ −0.5872. Switch it to degrees (DEG): tan 100° ≈ −5.6713. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also