Question

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?

Answer 1

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`.

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+(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`