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Thread: parameter restrictions HELP ??

  1. #1
    Junior Member
    Jun 2009

    parameter restrictions HELP ??

    hey, i just realli realli dont understand the restrictions for parameters in trig
    so for this question
    4. x = 2cos theta , y = 2sin theta
    and 0<theta<2 pi

    the equation is x squared +y squared = 4

    i understand that
    but then the restriction is -2>x>2 only

    i get that by drawing the cos graph there is a restriction on the y axis as the cos graph is between 2 and -2, but how du u no that the restriction is on the y axis and not on the x axis?
    AND why isnt there a restriction for the sin graph, ?? why isnt therre a restriction placed with y ?

    im SO LOST !!!
    any helpp apreciated !!
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  2. #2
    Senior Member Spec's Avatar
    Aug 2007
    Placing those restrictions on x will implicitly place the same restrictions on y, given the symmetry of the equation.

    $\displaystyle x^2+y^2=4\Longleftrightarrow y=\pm \sqrt{4-x^2}$ so we can see that y will have the same domain and range as x.

    Some further reading:

    Domain (mathematics) - Wikipedia, the free encyclopedia

    Range (mathematics) - Wikipedia, the free encyclopedia
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