Of course! Let's convert the given angle from radians to degrees step by step.
To convert radians to degrees, we use the conversion factor that [tex]\(180\)[/tex] degrees is equal to [tex]\(\pi\)[/tex] radians. The general formula to convert radians to degrees is:
[tex]\[
\text{Degrees} = \text{Radians} \times \left( \frac{180}{\pi} \right)
\][/tex]
Given the angle in radians is [tex]\(\frac{7\pi}{6}\)[/tex], let’s apply the formula:
1. First, we start with the given angle:
[tex]\[
\frac{7\pi}{6} \text{ radians}
\][/tex]
2. Apply the conversion factor:
[tex]\[
\text{Degrees} = \left( \frac{7\pi}{6} \right) \times \left( \frac{180}{\pi} \right)
\][/tex]
3. Notice that the [tex]\(\pi\)[/tex] terms cancel out each other:
[tex]\[
\text{Degrees} = \frac{7 \times 180}{6}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{7 \times 180}{6} = \frac{1260}{6} = 210
\][/tex]
So, the angle [tex]\(\frac{7\pi}{6}\)[/tex] radians is equivalent to [tex]\(210\)[/tex] degrees.
