Question

question 6 of 10 (1 point) | question attempt: 1 of 1
the unit circle is shown below. it has a circumference of $2\pi$.

• draw an arc that subtends a central angle of $\theta = \frac{5}{8} \cdot 2\pi$ radians.
• when you are done drawing the arc, find $s$, the length of the arc.

write your answer in terms of $\pi$. (you need not simplify your answer.)

Explanation:

Step1: Recall arc length formula

For a circle, arc length $s = r\theta$, where $r$ is radius, $\theta$ is central angle in radians. For unit circle, $r=1$, so $s=\theta$.

Step2: Substitute given angle

The central angle is $\theta = \frac{5}{8} \cdot 2\pi$.
<Expression>
$s = \frac{5}{8} \cdot 2\pi$
</Expression>

Answer:

$\frac{10}{8}\pi$ (or equivalently $\frac{5}{4}\pi$)

Note: For the drawing portion: start at the positive x-axis, draw an arc counterclockwise that spans $\frac{5}{8}$ of the full unit circle (5 out of the 8 equal marked segments around the circle).