Question

in this picture, the measure of angle $\theta$ is 1 radian.

a. true
b. false

Explanation:

Step1: Recall the definition of a radian

A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. The formula relating arc length \( s \), radius \( r \), and angle \( \theta \) (in radians) is \( s = r\theta \), which can be rearranged to \( \theta=\frac{s}{r} \).

Step2: Identify the radius and arc length

From the diagram, the radius \( r = 6 \) inches, and the arc length \( s = 6 \) inches (since the arc is marked as 6 in).

Step3: Calculate the angle in radians

Using the formula \( \theta=\frac{s}{r} \), substitute \( s = 6 \) and \( r = 6 \):
\[
\theta=\frac{6}{6}=1 \text{ radian}
\]

Answer:

A. True