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Thread: Graphs terminate with arrows

  1. #1

    Graphs terminate with arrows

    I notice that when graphing, at times the graph terminates at one or both ends with an arrow. For example, graphing polar equation f(theta) = 7 * cos (2.5 * theta) will result in a rose-type graph but with arrows at two ends. It appears to have something to do with the domain that Sketchpad uses to graph the function, but I'm not seeing where the domain can be changed. Any suggestions? Thanks.

  2. #2
    Hi Robert,
    Yes, I have a suggestion for you. The domain, and the appearance of arrowheads, are properties of the graph itself. So right-click (or ctrl-click) the graph and choose Properties. Then go to the Plot panel, where you can set the domain and also check or uncheck the box labeled "Show arrowheads and endpoints." The default domain for a graph in the form r = f(theta) is from 0 to 2π, but you can change that to be whatever you like.

    For instance, it's really interesting, with a rose graph, to set the domain to be 0 to π, and observe that f(theta) = sin (n*theta) always has exactly n nodes when n is an integer, with the nodes symmetrically distributed when n is odd and asymmetrically distributed when n is even.

    Related, have you used the Cartesian Graphs and Polar Graphs sketch in the Sample Activities? It provides a nice way to think about the relationship between the Cartesian graph of y = sin x and the polar graph of r = sin theta.

  3. #3
    Thank you, Scott. That worked and I will check out your suggested Sample Activities.

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