A circle has a center at $(3, 0)$ $(3 ,0 )$ and passes through $(0, 1)$ $(0 ,1 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

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A circle has a center at $(3, 0)$ $(3 ,0 )$ and passes through $(0, 1)$ $(0 ,1 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

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Answer 1 · 2016-02-04T06:58:48

$s \approx 7.451$ $s ~~ 7.451$

Explanation:

Arc length is computed using the formula $s = r \cdot θ$ $s = r * theta$

The center of the circle is on $(3, 0)$ $(3, 0)$ and it passes through $(0, 1)$ $(0, 1 )$ . Given these two points, we can determine the radius of the circle since we know that the radius is the distance from the center to any point on the circle.

[Solving for Radius]
Using the distance formula: $\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)$

$d = \sqrt{{(0 - 3)}^{2} + {(1 - 0)}^{2}}$ $d = sqrt((0-3)^2 + (1 - 0)^2)$
$d = \sqrt{{(- 3)}^{2} + {(1)}^{2}}$ $d = sqrt((-3)^2 + (1)^2)$
$d = \sqrt{9 + 1}$ $d = sqrt(9 + 1)$
$d = \sqrt{10}$ $d = sqrt(10)$

Using the arc length formula...

$s = \sqrt{10} \cdot \frac{3 π}{4}$ $s = sqrt10 * (3pi)/4$
$s \approx 7.451$ $s ~~ 7.451$

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A circle has a center at $(3, 0)$ $(3 ,0 )$ and passes through $(0, 1)$ $(0 ,1 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

1 Answer

Explanation:

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A circle has a center at (3,0)(3 ,0 ) and passes through (0,1)(0 ,1 ). What is the length of an arc covering 3π4(3pi ) /4 radians on the circle?

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A circle has a center at $(3, 0)$ $(3 ,0 )$ and passes through $(0, 1)$ $(0 ,1 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?