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Which of the following radian measures is equal to $540^\circ$ ? $\newline$ (The number of degrees of arc in a circle is $360^\circ$ . The number of radians of arc in a circle is $2\pi$ .) $\newline$ Choose $1$ answer: $\newline$ (A) $3\pi$ radians $\newline$ (B) $6\pi$ radians $\newline$ (C) $9\pi$ radians $\newline$ (D) $12\pi$ radians

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Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

540^\circ

?

\newline

(The number of degrees of arc in a circle is

360^\circ

. The number of radians of arc in a circle is

2\pi

.)

\newline

Choose

1

answer:

\newline

(A)

3\pi

radians

\newline

(B)

6\pi

radians

\newline

(C)

9\pi

radians

\newline

(D)

12\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 $180$ degrees is equal to $\pi$ radians. To convert degrees to radians, we use the formula: $\text{radians} = \text{degrees} \times (\pi/180)$ .
Convert $540$ Degrees: Convert $540$ degrees into radians using the formula from Step $1$ . By substituting $540$ degrees into the formula, we get: $540$ degrees $\times (\pi/180) = 3\pi$ radians.

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