# How do you convert #4=(x-4)^2+(y-1)^2# into polar form?

Now do all the replacement work.

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To convert the equation (4 = (x - 4)^2 + (y - 1)^2) into polar form, we use the following relationships between Cartesian and polar coordinates:

[ x = r \cos(\theta) ] [ y = r \sin(\theta) ]

Substitute these expressions into the given equation and simplify:

[ 4 = (r \cos(\theta) - 4)^2 + (r \sin(\theta) - 1)^2 ]

[ 4 = (r^2 \cos^2(\theta) - 8r\cos(\theta) + 16) + (r^2 \sin^2(\theta) - 2r\sin(\theta) + 1) ]

[ 4 = r^2 \cos^2(\theta) + r^2 \sin^2(\theta) - 8r\cos(\theta) - 2r\sin(\theta) + 17 ]

Using the trigonometric identity ( \cos^2(\theta) + \sin^2(\theta) = 1 ), the equation simplifies to:

[ 4 = r^2 - 8r\cos(\theta) - 2r\sin(\theta) + 17 ]

[ 0 = r^2 - 8r\cos(\theta) - 2r\sin(\theta) + 13 ]

This is the polar form of the equation.

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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.

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.

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.

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