On the unit circle centered at point $O$, which of the following best describes a central angle whose intercepted arc has a length equal to $1$ unit?

• A. The central angle measures $1$ degree.
• B. The central angle measures $90$ degrees.
• C. The central angle measures $2\pi$ radians.
• D. The central angle measures $1$ radian.

Answer: (D)

Verified step by step guidance

1. Recall the relationship between the length of an arc (s), the radius (r) of the circle, and the central angle (θ) in radians: \(s = r \times \theta\).
2. Since the circle is a unit circle, its radius \(r = 1\) unit.
3. Substitute \(r = 1\) and the given arc length \(s = 1\) unit into the formula: \$1 = 1 \times \theta$.
4. Solve for the central angle \(\theta\): \(\theta = 1\) radian.
5. Understand that this means the central angle whose intercepted arc length is 1 unit on a unit circle measures exactly 1 radian, not degrees or multiples of \(\pi\).