I understand the equation part, but I don't get the interval part. Please help me, please.?

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  • Alan
    Lv 7
    2 months ago

    Which interval part?  

    (For The original parametric equation that θ is between 0 and 2pi  

    or Are looking to restrict the resultant the rectangular equation?

      

    that θ is between 0 and 2pi  

    However, that does really matter since the graph is repeats itself. 

    Going from 2pi to 4pi gives you the same graph over again. 

    Going from 4pi to 6pi gives you the same graph over again 

    and so on

    Limiting the domain to 0 to 2pi just makes you complete the 

    graph once.   If you don't restrict the range, you just 

    trace over the same graph over and over again. 

    Sine and cosine are periodic function which repeat with a period of 2 pi 

    Also, there are no θ terms which are not sine and cosine.

    The resultant cartesian equation range and domain are restricted

    but you don't need to define it.  

    (x-2)^2/9 + (y+1)^2/4 = 1

    The above equation restricts the cartesian range all by itself. 

    This is an equation of an ellipse

    This is the equation

    of an ellipse centered at

    (2,-1) with semi-major axis of 3  and semi-minor axis of 2    

    focal length c = sqrt(5)

    You don't have to define a range restriction unless you are using it to graph 

    in a tool.

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  • sin(t) and cos(t) are bounded by -1 and 1

    3 * (-1) + 2 < x < 3 * 1 + 2

    -3 + 2 < x < 3 + 2

    -1 < x < 5

    2 * (-1) - 1 < y < 2 * 1 - 1

    -2 - 1 < y < 2 - 1

    -3 < y < 1

    EDIT

    Rather, it should be -1 </= x </= 5 and -3 </= y </= 1, with </= being less than or equal to

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