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What is the exact value of cot(5(pi)/6)?

  • MATH -

    = cos(5π/6) / sin(5π/6)
    = sin(π/2 - 5π/6)/ cos(π/2 - 5π/6)
    = sin(-π/3)/cos(-π/3)
    = -sin(π/3)/cos(π/3)
    = -(sqrt(3)/2)/(1/2)
    = -sqrt(3)

  • MATH -

    Use Google, if you don't have a calculator. Type
    tan(5*pi/6) =
    in the search box.
    Then take the reciprocal of that answer, for the cotangtent.
    You may recognize the answer as the square root of 3.

    5 pi/6 is a 150 degree angle. The reference angle is 30 degrees, but cosine is negative in the second quadrant.

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