Question

the radius of a circle is 1. what is the measure, in radians, of the angle subtended by an arc
\\( \frac { \pi } { 12 } \\) long?

give the exact answer in simplest form.

radians

Explanation:

Step1: Recall the arc - length formula

The formula for arc length \(s\) is \(s = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

We are given that \(s=\frac{\pi}{12}\) and \(r = 1\). Substituting into \(s=r\theta\), we get \(\frac{\pi}{12}=1\times\theta\).

Answer:

\(\frac{\pi}{12}\)