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what is the inverse tangent of negative root3/3

  • Precalc -

    let tan^-1 (-√3/3) = Ø

    then tanØ = -√3/3

    I know tan 30° or tan π/6 = +√3/3

    Ø must be in quadrants II or IV

    in degrees: Ø = 180-30=150° or Ø = 360-30 = 330°
    in radians: Ø = π - π/6 = 5π/6 or Ø = 2π-π/6 = 11π/6

    notice that your calculator gives you -30° or -π/6
    which is correct since -30° is coterminal with 330°

    calculators have been programmed to give the closest answer to zero, which in this case is -30°

    the smallest positive answer is 5π/6

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