Elise C.

# How do you convert a shifted parametric circle equation to rectangular form?

x=-2cos((1/2)t-(π/2))+23

y=2sin((1/2)t-(π/2))+6

specifically, how do you separate the stuff inside the cos/sin parenthesis to eliminate a parameter? I find all kinds of solved simple circle equations, but no shifted ones.

By:

Elise C.

What do you mean by wiggles? And does the shift not affect the final Cartesian equation?
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04/08/19 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

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