To convert a given angle from radians to degrees, we use the following conversion factor:
[tex]\[ \text{Degrees} = \text{Radians} \times \left( \frac{180}{\pi} \right) \][/tex]
Given the angle in radians is [tex]\(\frac{7 \pi}{3}\)[/tex], we can apply this conversion factor as follows:
1. Start with the given radians:
[tex]\[ \text{Radians} = \frac{7 \pi}{3} \][/tex]
2. Multiply the radians by [tex]\(\frac{180}{\pi}\)[/tex] to convert to degrees:
[tex]\[ \text{Degrees} = \frac{7 \pi}{3} \times \left( \frac{180}{\pi} \right) \][/tex]
3. Simplify the expression by cancelling [tex]\(\pi\)[/tex] from the numerator and denominator:
[tex]\[ \text{Degrees} = \frac{7 \times 180}{3} \][/tex]
4. Perform the multiplication and division:
[tex]\[ \text{Degrees} = \frac{1260}{3} \][/tex]
5. Simplify the result:
[tex]\[ \text{Degrees} = 420.0 \][/tex]
Thus, [tex]\(\frac{7 \pi}{3}\)[/tex] radians is equal to [tex]\(420\)[/tex] degrees.
Answer: [tex]\( 420 \)[/tex] degrees
