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Which of the following radian measures is equal to
1,080^(@) ?
(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
3pi radians
(B)
6pi radians
(C)
10 pi radians
(D)
12 pi radians

Which of the following radian measures is equal to $1,080^{\circ}$ ? $\newline$ (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) $3 \pi$ radians $\newline$ (B) $6 \pi$ radians $\newline$ (C) $10 \pi$ 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

1,080^{\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)

3 \pi

radians

\newline

(B)

6 \pi

radians

\newline

(C)

10 \pi

radians

\newline

(D)

12 \pi

radians

Understanding degrees and radians: 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, or $\frac{\pi}{180}$ radians.
Converting degrees to radians: Convert $1,080$ degrees to radians using the relationship from Step $1$ . Multiply $1,080$ degrees by $\frac{\pi}{180}$ to find the equivalent in radians. $\newline$ Calculation: $1,080 \times \left(\frac{\pi}{180}\right) = 6 \times \pi$
Simplifying the calculation: Simplify the calculation to find the final answer. $1,080 \times (\pi/180)$ simplifies to $6\pi$ because $1,080$ divided by $180$ equals $6$ . $\newline$ Calculation: $6 \times \pi = 6\pi$ radians
Choosing the correct option: Choose the correct option from the given choices that matches the calculated radian measure. $\newline$ The correct option is (B) $6\pi$ radians.

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\newline

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