URGENT:How can I find a curves orientation?I neeed to know before my exam?

like in this question X=8cos@ Y=8sin@

I know I get a circle for the graph, but not sure why the orientation is counterclockwise?????

Not only in this question but in all questions when it says what is the orientation of the curve, I get lost:(

1 Answer

  • 8 years ago
    Favorite Answer

    The "all questions" part is hard. In cases like this, though, you can lean on the conversion formula:

    x = r cos θ

    y = r sin θ

    ...where r is the distance from the origin and θ is the *counterclockwise* angle from the +x axis. So anything you can get into the form of:

    x = r1 cos (aθ + b)

    y = r2 sin (aθ + b)

    ... will have counter-clockwise orientation if a>0 and clockwise orientation if a<0, provided that r1 and r2 are both positive (or both negative) throughout.

    If you get a head-scratcher, plot a few points to get a sense of what's going on, if you have time to get back to it before time is up. Obviously, you don't want to stay stuck on one problem in an exam.

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