Question

the radius of a circle is 1. what is the length of an arc that subtends an angle of \frac{\pi}{4} 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

Given \(r = 1\) and \(\theta=\frac{\pi}{4}\). Substitute these values into the formula \(s=r\theta\). So, \(s=(1)\times\frac{\pi}{4}\).

Answer:

\(\frac{\pi}{4}\)