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17 April, 05:33

Find the solution set of the given equation for 0 ≤ x ≤ 2π.

3cotx = sqrt3

+3
Answers (1)
  1. 17 April, 05:48
    0
    Step-by-step explanation:

    Answer:

    x

    =

    π

    6

    +

    n

    2

    π

    ,

    7

    π

    6

    +

    n

    2

    π

    , where n is an integer

    Explanation:

    Start with:

    cot

    x

    -



    3

    =

    0

    cot

    x

    =



    3

    This means that:

    cos

    x

    sin

    x

    =



    3

    1

    So the adjacent is length



    3

    and the opposite is length 1. This set us up for the 30/60/90 triangle and the angle we're looking at is the

    30

    o

    or

    π

    6

    one.

    So now the question is which quadrants are we looking at. Cotangent is positive in Q1 and Q3. The angles we're looking at, then, are

    π

    6

    and

    π

    +

    π

    6

    =

    7

    π

    6

    .

    This question does not limit our answer to any particular domain, and so we need the general solution, which is:

    x

    =

    π

    6

    +

    n

    2

    π

    ,

    7

    π

    6

    +

    n

    2

    π

    , where n is an integer
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