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Chapter 4: Problem 27

What angle corresponds to a circular arc on the unit circle with length \(\frac{\pi}{5} ?\)

Short Answer

Expert verified
The angle that corresponds to a circular arc length of \(\frac{\pi}{5}\) on the unit circle is \(\boxed{\frac{\pi}{5}}\).

Step by step solution

01

Write down the arc length formula

We will use the arc length formula, \(s = r \theta\), to find the angle \(\theta\). Since we are working with a unit circle, the radius \(r=1\), and the formula simplifies to \(s = \theta\).
02

Plug in the given arc length value

We are given the arc length value \(s = \frac{\pi}{5}\). Substituting this value into the formula, we get: \(\frac{\pi}{5} = \theta\).
03

Solve for the angle \(\theta\)

Since the angle \(\theta\) is already isolated on one side of the equation, we have found our answer: \(\theta = \frac{\pi}{5}\). Thus, the angle that corresponds to a circular arc length of \(\frac{\pi}{5}\) on the unit circle is \(\boxed{\frac{\pi}{5}}\).

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