could someone explain how sine^2 +cos^2 =1 can prove (x-3)^2+ (y-5)^2 =4.
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Are you once again thinking about parametric presentations of the circle (x-3)^2+ (y-5)^2 =4? If so they are: x(t)=2cos(t)+3 & y(t)=2sin(t)+5. Just substitute in the original and you will see how it works.
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