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Convert the radian measure to degrees. Give the answer using decimal degrees to the nearest hundredth. Use 3.1416 for [tex]\pi[/tex].

[tex]5[/tex] radians

A. [tex]286.48^{\circ}[/tex]
B. [tex]286.78^{\circ}[/tex]
C. [tex]572.96^{\circ}[/tex]
D. [tex]572.65^{\circ}[/tex]



Answer :

GinnyAnswer
To convert radians to degrees, we use the formula:

[tex]\[ \text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right) \][/tex]

Given the radian measure is [tex]\(5\)[/tex] and [tex]\(\pi\)[/tex] is approximated as [tex]\(3.1416\)[/tex], we can substitute these values into the formula.

First, calculate the conversion factor:

[tex]\[ \frac{180}{\pi} = \frac{180}{3.1416} \][/tex]

Next, multiply the given radian measure by this conversion factor:

[tex]\[ \text{degrees} = 5 \times \left(\frac{180}{3.1416}\right) = 5 \times 57.2958 \][/tex]

Perform multiplication:

[tex]\[ \text{degrees} = 286.4782 \][/tex]

We need to round this result to the nearest hundredth:

[tex]\[ \text{Rounded degrees} = 286.48 \][/tex]

Therefore, the radian measure of 5 radians converts to approximately [tex]\(286.48^{\circ}\)[/tex] when rounded to the nearest hundredth.

Out of the provided options, [tex]\(286.48^{\circ}\)[/tex] is the correct answer.

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