We are asked to complete each table converting the given measure to its equivalent measure in degrees or radians
Degrees to Radians:
We use the following relation to convert from degrees to radians
[tex]\text{radian}=\frac{2\pi}{360\degree}\times\text{degree}[/tex]Radians to Degrees:
We use the following relation to convert from radians to degrees
[tex]\text{degree}=\frac{360\degree}{2\pi}\times\text{radian}[/tex]Now let us perform the conversions
Table 1:
[tex]\begin{gathered} \text{radian}=\frac{2\pi}{360\degree}\times\text{degree} \\ \text{radian}=\frac{2\pi}{360\degree}\times0\degree \\ \text{radian}=0 \end{gathered}[/tex][tex]\begin{gathered} \text{radian}=\frac{2\pi}{360\degree}\times\text{degree} \\ \text{radian}=\frac{2\pi}{360\degree}\times30\degree \\ \text{radian}=\frac{\pi}{6} \end{gathered}[/tex][tex]\begin{gathered} \text{degree}=\frac{360\degree}{2\pi}\times\text{radian} \\ \text{degree}=\frac{360\degree}{2\pi}\times\frac{\pi}{4} \\ \text{degree}=45\degree \end{gathered}[/tex][tex]\begin{gathered} \text{degree}=\frac{360\degree}{2\pi}\times\text{radian} \\ \text{degree}=\frac{360\degree}{2\pi}\times\frac{\pi}{2} \\ \text{degree}=90\degree \end{gathered}[/tex]Table 2:
[tex]\begin{gathered} \text{degree}=\frac{360\degree}{2\pi}\times\text{radian} \\ \text{degree}=\frac{360\degree}{2\pi}\times\frac{2\pi}{3} \\ \text{degree}=120\degree \end{gathered}[/tex][tex]\begin{gathered} \text{degree}=\frac{360\degree}{2\pi}\times\text{radian} \\ \text{degree}=\frac{360\degree}{2\pi}\times\pi \\ \text{degree}=180\degree \end{gathered}[/tex][tex]\begin{gathered} \text{radian}=\frac{2\pi}{360\degree}\times\text{degree} \\ \text{radian}=\frac{2\pi}{360\degree}\times270\degree \\ \text{radian}=\frac{3\pi}{2} \end{gathered}[/tex]Therefore, both the tables have been completed with degrees and radians values.
