A circle's center is at $(3 ,4 )$ and it passes through $(3 ,2 )$ . What is the length of an arc covering $( pi ) /6$ 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 $(2pi)/6$ $units$ .

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:

$r=sqrt((x_2-x_1)^2+(y_2-y_1)^2) = sqrt((3-3)^2+(2-4)^2)=2$ $units$

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

$(pi/6)/(2pi)*4pi = (2pi)/6$

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 ( pi ) /6 ( pi ) /6 radians on the circle?