To convert radians to degrees, we need to use the relationship between these two units. We know that [tex]\( \pi \)[/tex] radians are equivalent to 180 degrees. Therefore, to convert radians to degrees, we can use the formula:
[tex]\[ \text{degrees} = \text{radians} \times \left( \frac{180}{\pi} \right) \][/tex]
For the given problem, we need to determine how many degrees are equivalent to [tex]\( \frac{29 \pi}{18} \)[/tex] radians.
1. First, identify the number of radians:
[tex]\[
\text{radians} = \frac{29 \pi}{18}
\][/tex]
2. Use the conversion factor between radians and degrees:
[tex]\[
\text{degrees} = \text{radians} \times \left( \frac{180}{\pi} \right)
\][/tex]
3. Substitute [tex]\(\frac{29 \pi}{18}\)[/tex] in place of radians:
[tex]\[
\text{degrees} = \frac{29 \pi}{18} \times \left( \frac{180}{\pi} \right)
\][/tex]
4. Cancel out [tex]\(\pi\)[/tex] from the numerator and denominator:
[tex]\[
\text{degrees} = \frac{29 \times 180}{18}
\][/tex]
5. Simplify the fraction:
[tex]\[
\frac{29 \times 180}{18} = 29 \times 10 = 290
\][/tex]
So, [tex]\(\frac{29 \pi}{18}\)[/tex] radians are equal to 290 degrees.
Therefore, the correct answer is:
290
