How Do I Create/Plot Array of Calculated Values

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I've chosen some values to have something to work with. Go to a Sage Cell Server and copy/paste the following code in:

m = 5
r = 3
w = 6
x_coords = [t for t in range(0,360,5)]
y_coords = [m*r*w^2*cos(t*pi/180).n(digits=5) for t in range(0,360,5)]
list_plot([(x_coords[i],y_coords[i]) for i in range(0,len(x_coords))])

Press "Evaluate" and you'll get the plot. Creating the arrays: The first array (actually a list in Python) has the x coordinates, the second list creates the y values. Note that range(0,360,5) will not include 360. Plotting the data: list_plot is used to graph the points. The len(x_coords) is the length of the list (number of x values).

To complement @dazedANDconfused answer, which is correct, you can first notice that you do not need to write arrays (they are named lists in Python) if you only want to plot the function, you can simply do:

sage: m = 5
sage: r = 3
sage: w = 6
sage: f(t) = m*r*w^2*cos(t*pi/180)
sage: plot(f, t, 0, 360)

Second, if you want to deal with X and Y lists, you can use the Python zip function to avoid iterating among indexes 0...len(x_coords)-1 by hand:

sage: zip([1,2,3],[4,5,6])
[(1, 4), (2, 5), (3, 6)]

So in your case, you can write the less verbose:

sage: list_plot(zip(x_coords,y_coords))

The following also works:

sage: points(zip(x_coords,y_coords))

The answers by @dazedANDconfused and @tmonteil are correct.

To save time if you were doing computations on a larger scale, you could also

• use a numerical value for pi instead of the symbolic version of pi,
• calculate $mrw^2$ once and for all,
• calculate the ratio pi/180 once and for all,
• use a lambda function instead of a symbolic function.

Combining those, you could write:

sage: m, r, w = 5, 3, 6
sage: mrw2 = m * r * w^2
sage: deg_rad = RDF.pi() / 180    # degree to radian conversion factor
sage: ff = lambda t: mrw2 * cos(t * deg_rad)
sage: plot(ff, 0, 360)

Of course, this is a bit pointless here: who cares if it takes 4 ms or 40 ms for computing the plot, when displaying the plot takes much longer than that.