# A circle's center is at #(2 ,1 )# and it passes through #(3 ,2 )#. What is the length of an arc covering #(5pi ) /12 # radians on the circle?

Length of arc covering

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The length of an arc on a circle is given by the formula ( s = r \cdot \theta ), where ( s ) is the arc length, ( r ) is the radius of the circle, and ( \theta ) is the central angle in radians.

Given that the circle's center is at (2, 1) and it passes through (3, 2), we can find the radius using the distance formula:

[ r = \sqrt{(3 - 2)^2 + (2 - 1)^2} = \sqrt{1 + 1} = \sqrt{2} ]

The angle ( \theta ) corresponding to ( \frac{5\pi}{12} ) radians can be calculated as:

[ \theta = \frac{5\pi}{12} ]

Thus, the length of the arc is:

[ s = (\sqrt{2}) \cdot \frac{5\pi}{12} \approx 1.307 \text{ units} ]

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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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