What's the center in the x direction? What's the center in the y direction? What's the radius.
the x part is centered at 23 and wiggles back and forth, +/- 2
the y part is centered at 6 and wiggles back and forth, +/- 2
So the radius is 2. The center is at (23,6), and the cartesian equation is:
(x-23)^2 + (y-6)^2 = 2^2
K.J. P.
tutor
Cos and Sin both oscillate back and forth between -1 and 1. So -2cos((1/2)t-(π/2)) oscillates back and forth between 2 and -2 as the argument goes from 0 to π to 2π to 3π, etc. The exact value of t affects where you would be on the circle at any particular time, but it doesn't affect the path that gets followed as t increases.
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04/08/19
K.J. P.
tutor
You can type parametric plot (-2cos((1/2)t-(π/2))+23, 2sin((1/2)t-(π/2))+6) into Wolfram Alpha and it will give you the picture.
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04/08/19
Elise C.
What do you mean by wiggles? And does the shift not affect the final Cartesian equation?04/08/19