Question

angle ( \theta ) is measured in radians.
what is the length of the arc subtended by the angle ( \theta )?
( \bigcirc ) a. ( \frac{3}{4} ) units
( \bigcirc ) b. ( \frac{3}{2} ) units
( \bigcirc ) c. ( \frac{3pi}{4} ) units
( \bigcirc ) d. ( \frac{3pi}{2} ) units

Explanation:

Step1: Identify radius and angle

The circle is a unit circle, so $r=1$. The angle $\theta$ spans 3 quadrants, so $\theta = \frac{3\pi}{2}$ radians.

Step2: Apply arc length formula

Arc length $s = r\theta$. Substitute $r=1$ and $\theta=\frac{3\pi}{2}$.
<Expression>
$s = 1 \times \frac{3\pi}{2} = \frac{3\pi}{2}$
</Expression>

Answer:

D. $\frac{3\pi}{2}$ units