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
3 5 3 0 0
3 5 2.60 2.5 0.52
3 5 1.5 4.33 1.05
3 5 0 5 1.57
3 5 -1.5 4.33 2.09
3 5 -2.60 2.5 2.62
3 5 -3 0 3.14
3 5 -2.60 -2.5 3.67
3 5 -1.5 -4.33 4.19
3 5 0 -5 4.71
3 5 1.5 -4.33 5.24
3 5 2.60 -2.5 5.76
3 5 3 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 y-axis where the maximum value is 5, whereas the minor axis will be on the x-axis where the maximum value is 3.

 

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