Question

the radius of a circle is 1. what is the length of an arc that subtends an angle of \frac{35\pi}{24} 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 that \(r = 1\) and \(\theta=\frac{35\pi}{24}\). Substitute these values into the formula \(s=r\theta\). Then \(s = 1\times\frac{35\pi}{24}\).

Answer:

\(\frac{35\pi}{24}\)