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15 August, 18:26

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

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  1. 15 August, 19:50
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    The answer

    ellipse main equatin is as follow:

    X² / a² + Y² / b² = 1, where a≠0 and b≠0

    for the first equation: x = 3 cos t and y = 8 sin t

    we can write x² = 3² cos² t and y² = 8² sin² t

    and then x² / 3² = cos² t and y²/8² = sin² t

    therefore, x² / 3² + y²/8² = cos² t + sin² t = 1

    equivalent to x² / 3² + y²/8² = 1

    for the second equation, x = 3 cos 4t and y = 8 sin 4t we found

    x² / 3² + y²/8² = cos² 4t + sin² 4t=1
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