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

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Answer 1 · 2016-03-07T06:44:35

$s = r θ = 2 \sqrt{2} \cdot \frac{π}{3} = 2.96192$ $s=rtheta=2sqrt2*pi/3=2.96192 " "$ units

The length of arc is given $s = r θ$ $s=r theta$ where $r =$ $r=$ radius, $θ =$ $theta=$ central angle in radian

compute $r = \sqrt{{(4 - 2)}^{2} + {(6 - 4)}^{2}} = 2 \sqrt{2}$ $r=sqrt((4-2)^2+(6-4)^2)=2sqrt2$

$θ = \frac{π}{3}$ $theta=pi/3$

$s = r θ = 2 \sqrt{2} \cdot \frac{π}{3} = 2.96192$ $s=rtheta=2sqrt2*pi/3=2.96192 " "$ units

God bless...I hope the explanation is useful.

A circle's center is at (4,6)(4 ,6 ) and it passes through (2,4)(2 ,4 ). What is the length of an arc covering π3(pi ) /3 radians on the circle?