Questions: In a unit circle, the radian measure of the central angle is equal to the length of the Choose the correct answer below. A. diameter of the circle B. intercepted arc C. radius of the circle

In a unit circle, the radian measure of the central angle is equal to the length of the

Choose the correct answer below. A. diameter of the circle B. intercepted arc C. radius of the circle

Transcript text: In a unit circle, the radian measure of the central angle is equal to the length of the $\qquad$ Choose the correct answer below. A. diameter of the circle B. intercepted arc C. radius of the circle

Solution

Solution Steps

To determine the correct answer, we need to recall the definition of a radian in the context of a unit circle. 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. In a unit circle, the radius is 1 unit.

Solution Approach

The radian measure of the central angle in a unit circle is equal to the length of the intercepted arc.

Step 1: Understanding Radians

In a unit circle, the radius $ r $ is defined as $ 1 $. The radian measure of a central angle $ \theta $ is defined as the angle subtended at the center of the circle by an arc whose length is equal to the radius.

Step 2: Relating Radians to Arc Length

Since the radius of the unit circle is $ 1 $, the length of the intercepted arc corresponding to the central angle $ \theta $ is also $ 1 $. Therefore, we have: \[ \theta = \text{length of intercepted arc} = 1 \]

Step 3: Conclusion

Thus, the radian measure of the central angle in a unit circle is equal to the length of the intercepted arc.