The following two sets of parametric functions both represent the same ellipse. explain the difference between the graphs.

x = 3 cos t and y = 8 sin t
x = 3 cos 4t and y = 8 sin 4t

Answer with explanation:

The two parametric equation of the same ellipse is

x = 3 cos t and y = 8 sin t

x = 3 cos 4 t and y = 8 sin 4 t

This is the equation of same ellipse, having different Parametric forms.

→The function involving , 3 cos t and 8 sin t has maximum value, 3 and 8,respectively , and a period of π  , whereas, the function  3 cos 4 t and , 8 sin 4 t , has also same maximum value, 3 and 8,respectively , but period changes , the period after which cycle of trigonometric function  sin 4 t and cos 4 t  repeats is, .

→x = 3 cos t and y = 8 sin t

→x = 3 cos 4 t and y = 8 sin 4 t

Also, these are equation of two lines having different slopes both passing through the origin.

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step-by-step explanation: