A circle's center is at $(3, 4)$ $(3 ,4 )$ and it passes through $(3, 2)$ $(3 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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A circle's center is at $(3, 4)$ $(3 ,4 )$ and it passes through $(3, 2)$ $(3 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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Answer 1 · 2016-02-15T11:16:30

We need to find the radius of the circle and use it to calculate a fraction of the circumference. The distance is $\frac{2 π}{6}$ $(2pi)/6$ $u n i t s$ $units$ .

Explanation:

First find the radius: we know the location of the center and of one point on the edge, so the radius is simply the distance between those points:

$r = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}} = \sqrt{{(3 - 3)}^{2} + {(2 - 4)}^{2}} = 2$ $r=sqrt((x_2-x_1)^2+(y_2-y_1)^2) = sqrt((3-3)^2+(2-4)^2)=2$ $u n i t s$ $units$

The circumference of the whole circle, which is $2 π$ $2pi$ radians, is $2 \cdot π \cdot r = 4 π$ $2*pi*r=4pi$ units. We want a fraction of that:

$\frac{\frac{π}{6}}{2 π} \cdot 4 π = \frac{2 π}{6}$ $(pi/6)/(2pi)*4pi = (2pi)/6$

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A circle's center is at $(3, 4)$ $(3 ,4 )$ and it passes through $(3, 2)$ $(3 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at $(3, 4)$ $(3 ,4 )$ and it passes through $(3, 2)$ $(3 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?