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Which of the following radian measures is equal to
2,880^(@) ?
(The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is
2pi.)
Choose 1 answer:
A
4pi radians
(B)
8pi radians
(C)
12 pi radians
(D)
16 pi radians

Which of the following radian measures is equal to $2,880^{\circ}$ ? $\newline$ (The number of degrees of arc in a circle is $360$ . The number of radians of arc in a circle is $2 \pi$ .) $\newline$ Choose $1$ answer: $\newline$ (A) $4 \pi$ radians $\newline$ (B) $8 \pi$ radians $\newline$ (C) $12 \pi$ radians $\newline$ (D) $16 \pi$ radians

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Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

2,880^{\circ}

?

\newline

(The number of degrees of arc in a circle is

360

. The number of radians of arc in a circle is

2 \pi

.)

\newline

Choose

1

answer:

\newline

(A)

4 \pi

radians

\newline

(B)

8 \pi

radians

\newline

(C)

12 \pi

radians

\newline

(D)

16 \pi

radians

Understand Relationship: Understand the relationship between degrees and radians. We know that $360$ degrees is equal to $2\pi$ radians. This means that $1$ degree is equal to $\frac{2\pi}{360}$ radians, which simplifies to $\frac{\pi}{180}$ radians.
Convert Degrees to Radians: Convert $2,880$ degrees to radians. Using the conversion factor from Step $1$ , we multiply $2,880$ degrees by $\pi/180$ radians/degree to find the equivalent in radians. $\newline$ $2,880$ degrees $\times (\pi/180$ radians/degree) $= (2,880/180) \times \pi$ radians $= 16 \times \pi$ radians.
Choose Correct Option: Choose the correct option that matches our calculation. The correct option is $16\pi$ radians, which is equivalent to $2,880$ degrees.

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