Question

if $r = 1$ and $\theta = \frac{5\pi}{4}$, what is the approximate arc length?

a. 3.927 units
b. 3.665 units
c. 1.25 units
d. 4.189 units

Explanation:

Step1: Recall arc length formula

The formula for arc length \( s \) when the central angle \( \theta \) is in radians is \( s = r\theta \).

Step2: Substitute given values

We know \( r = 1 \) and \( \theta=\frac{5\pi}{4} \). Substitute these into the formula: \( s = 1\times\frac{5\pi}{4}=\frac{5\pi}{4} \).

Step3: Calculate the numerical value

Using \( \pi\approx3.1416 \), we have \( \frac{5\times3.1416}{4}=\frac{15.708}{4} = 3.927 \).

Answer:

A. 3.927 units