# A circle has a center at #(1 ,2 )# and passes through #(4 ,2 )#. What is the length of an arc covering #pi /4 # radians on the circle?

I found

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To find the length of an arc covering (\frac{\pi}{4}) radians on the circle with a center at ((1, 2)) and passing through ((4, 2)), follow these steps:

- Find the radius of the circle using the distance formula between the center ((1, 2)) and a point on the circle ((4, 2)).
- Use the formula for the circumference of a circle to find the total circumference.
- Calculate the length of the arc by multiplying the fraction of the circumference corresponding to (\frac{\pi}{4}) radians.

Let's go through the calculations:

- Radius = (\sqrt{(4 - 1)^2 + (2 - 2)^2} = \sqrt{3^2 + 0^2} = 3).
- Circumference = (2\pi \times \text{radius} = 2\pi \times 3 = 6\pi).
- Length of arc (= \frac{\text{arc angle}}{2\pi} \times \text{circumference}). Length of arc (= \frac{\frac{\pi}{4}}{2\pi} \times 6\pi = \frac{1}{8} \times 6\pi = \frac{3\pi}{4}).

Therefore, the length of the arc covering (\frac{\pi}{4}) radians on the circle is (\frac{3\pi}{4}) 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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