Question

Complete each table converting the given measure to its equivalent measure in degrees or radians.

Answer 1

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

`\text{radian}=(2\pi)/(360\degree)*\text{degree}`

Radians to Degrees:

We use the following relation to convert from radians to degrees

`\text{degree}=(360\degree)/(2\pi)*\text{radian}`

Now let us perform the conversions

Table 1:

`\begin{gathered} \text{radian}=(2\pi)/(360\degree)*\text{degree} \\ \text{radian}=(2\pi)/(360\degree)*0\degree \\ \text{radian}=0 \end{gathered}`
`\begin{gathered} \text{radian}=(2\pi)/(360\degree)*\text{degree} \\ \text{radian}=(2\pi)/(360\degree)*30\degree \\ \text{radian}=(\pi)/(6) \end{gathered}`
`\begin{gathered} \text{degree}=(360\degree)/(2\pi)*\text{radian} \\ \text{degree}=(360\degree)/(2\pi)*(\pi)/(4) \\ \text{degree}=45\degree \end{gathered}`
`\begin{gathered} \text{degree}=(360\degree)/(2\pi)*\text{radian} \\ \text{degree}=(360\degree)/(2\pi)*(\pi)/(2) \\ \text{degree}=90\degree \end{gathered}`

Table 2:

`\begin{gathered} \text{degree}=(360\degree)/(2\pi)*\text{radian} \\ \text{degree}=(360\degree)/(2\pi)*(2\pi)/(3) \\ \text{degree}=120\degree \end{gathered}`
`\begin{gathered} \text{degree}=(360\degree)/(2\pi)*\text{radian} \\ \text{degree}=(360\degree)/(2\pi)*\pi \\ \text{degree}=180\degree \end{gathered}`
`\begin{gathered} \text{radian}=(2\pi)/(360\degree)*\text{degree} \\ \text{radian}=(2\pi)/(360\degree)*270\degree \\ \text{radian}=(3\pi)/(2) \end{gathered}`

Therefore, both the tables have been completed with degrees and radians values.