To convert radians to degrees, we use the conversion factor [tex]\( \frac{180}{\pi} \)[/tex]. This factor arises from the relationship between radians and degrees; there are [tex]\( \pi \)[/tex] radians in [tex]\( 180 \)[/tex] degrees.
Step-by-step solution:
1. Identify the given value in radians:
[tex]\[
8.6149 \text{ radians}
\][/tex]
2. Use the conversion factor to convert radians to degrees:
[tex]\[
\text{Degrees} = \text{Radians} \times \left( \frac{180}{\pi} \right)
\][/tex]
3. Substitute the value [tex]\( 8.6149 \)[/tex] radians into the conversion formula:
[tex]\[
\text{Degrees} = 8.6149 \times \left( \frac{180}{\pi} \right)
\][/tex]
4. Calculate the result:
[tex]\[
\text{Degrees} \approx 493.59741092725295
\][/tex]
Therefore, [tex]\( 8.6149 \)[/tex] radians is approximately [tex]\( 493.59741092725295 \)[/tex] degrees.
