Trig

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find all solutions to the equation √3 csc(2theta)=-2

Would the answer be
π/6 + 2πn, 5π/6 +2πn or π/6 + πn, 5π/6 +πn?

or neither?

  • Trig -

    sqrt ( 3 ) * csc ( 2 theta ) = - 2 Divide both sides by sqrt ( 3 )

    csc ( 2 theta ) = - 2 / sqrt ( 3 )

    Take the inverse cosecant of both sides.

    2 theta = - pi / 3

    and

    2 theta = 4 pi / 3


    [ Becouse csc ( pi / 3 ) = 2 / sqrt ( 3 ) , and csc ( 4 pi / 3 = 2 / sqrt ( 3 ) ]


    Divide both sides by 2

    theta = - pi / 6

    and

    theta = 2 pi / 3


    Period of csc ( theta ) = 2 pi

    So period of 2 theta = 2 pi / 2 = pi


    Final solutions :

    theta = n pi + 2 pi / 3 = pi ( n + 2 / 3 )

    and

    theta = n pi - pi / 6 = pi ( n - 1 / 6 )

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