Excel Interpretation of the Parametric Equations


When a > b the follwoing worksheet was used to determine the chart:

a*cos(t)

b*sin(t)

a

b

x

y

t
5 3 5 0 0
5 3 4.33 1.49 0.52
5 3 2.50 2.60 1.05
5 3 0 3.00 1.57
5 3 -2.48 2.60 2.09
5 3 -4.33 1.50 2.62
5 3 -5 0 3.14
5 3 -4.32 -1.51 3.67
5 3 -2.49 -2.60 4.19
5 3 0 -3.00 4.71
5 3 2.52 -2.60 5.24
5 3 4.33 -1.50 5.76
5 3 5 0 6.28

The highlighted rows indicate the x-intercepts and y-intercepts of the graph, examine the symmetry over the x-axis and y-axis. Observe that the major axis will be on the x-axis where the maximum value is 5, whereas the minor axis will be on the y-axis where the maximum value is 3.

 

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