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    Tan 75 Degrees

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

    What is tan 75°?

    Answer

    tan 75° =
    2 + √3 ≈ 3.7321

    Angle in radians: 75° = 5π/12. The point of the angle is in quadrant I, where tangent is positive.

    ≈ — rounded to 4 decimal places.

    tan 75° = sin 75° / cos 75° = ((√6 + √2)/4) / ((√6 − √2)/4) = 2 + √3

    tan 75° = tan(45° + 30°) = (1 + √3/3) / (1 − √3/3) = 2 + √3

    xyOP

    P(cos 75°, sin 75°) ≈ (0.2588, 0.9659)

    T(1, tan 75°) ≈ (1, 3.7321) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

    All four functions of 75°
    FunctionExact valueDecimal
    sin 75°(√6 + √2)/4≈ 0.9659
    cos 75°(√6 − √2)/4≈ 0.2588
    tan 75°2 + √3≈ 3.7321
    cot 75°2 − √3≈ 0.2679

    See Also

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    https://calculat.io/en/number/trigonometry/tan--75Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--75">Tan 75 Degrees: Tangent of 75° on the Unit Circle</a>Copy
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    Tan 75 Degrees: Tangent of 75° on the Unit Circle. tan 75° = 2 + √3 ≈ 3.7321. The tangent is the ratio y/x of the point at 75° on the unit circle.
    https://calculat.io/en/number/trigonometry/tan--75/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    72°√(5 + 2√5)
    73°≈ 3.2709
    74°≈ 3.4874
    75°2 + √3
    76°≈ 4.0108
    77°≈ 4.3315
    78°≈ 4.7046
    Recalculate with different values ↑

    FAQ

    What is tan 75°?

    tan 75° = 2 + √3 ≈ 3.7321

    How are sin 15° and cos 75° related?

    They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

    Why does a calculator show −0.4207 for tan 75?

    The calculator is in radian mode (RAD): it takes tan 75 as the tangent of 75 radians, tan 75 rad ≈ −0.4207. Switch it to degrees (DEG): tan 75° = 2 + √3 ≈ 3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also