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How do you find cartesian equation the parametric equations of a circle are #x=cos theta -4# and #y=sin theta + 1#?

Answer 1

Christopher Agresta

#(x+4)^2+(y-1)^2=1#

From #x=cos(theta)-4#, #cos(theta)=x+4# and from #y=sin(theta)+1#, #sin(theta)=y-1#

Hence,

#(x+4)^2+(y-1)^2=(cos(theta))^2+(sin(theta))^2# or,

#(x+4)^2+(y-1)^2=1#

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Answer 2

Paisley Johnson

To find the Cartesian equation of the parametric equations of a circle given by ( x = \cos(\theta) - 4 ) and ( y = \sin(\theta) + 1 ), square both equations and then add them together. Utilize the trigonometric identity ( \cos^2(\theta) + \sin^2(\theta) = 1 ). After simplification, the Cartesian equation of the circle will be ( (x + 4)^2 + (y - 1)^2 = 1 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.