Question

the radius of a circle is 3. what is the length of an arc that subtends an angle of \frac{\pi}{5} radians? give the exact answer in simplest form.

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) of a circle 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

Given \(r = 3\) and \(\theta=\frac{\pi}{5}\). Substitute these values into the formula \(s=r\theta\). So \(s = 3\times\frac{\pi}{5}\).

Answer:

\(\frac{3\pi}{5}\)