To convert from radians to degrees, we use the formula:
[tex]\[
\text{degrees} = \text{radians} \times \frac{180}{\pi}
\][/tex]
This formula comes from the fact that [tex]\(\pi\)[/tex] radians is equivalent to [tex]\(180^{\circ}\)[/tex]. Therefore, multiplying the number of radians by [tex]\(\frac{180^{\circ}}{\pi}\)[/tex] will give us the equivalent measure in degrees.
Given the question, we are converting 8 radians to degrees. We will use the expression from the formula:
[tex]\[
\text{degrees} = 8 \times \frac{180}{\pi}
\][/tex]
To identify the correct expression from the given options:
A. [tex]\(8 \pi\)[/tex]
B. [tex]\(\frac{\pi}{180^{\circ}}\)[/tex]
C. [tex]\(8 \times 180^{\circ}\)[/tex]
D. [tex]\(\frac{180^{\circ}}{\pi}\)[/tex]
Option D, [tex]\(\frac{180^{\circ}}{\pi}\)[/tex], is the conversion factor we need to multiply by the given radians. Thus, the correct expression to convert 8 radians to degrees is:
[tex]\[
8 \times \frac{180^{\circ}}{\pi}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{180^{\circ}}{\pi}}
\][/tex]
