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Which of the following radian measures is equal to
240^(@) ?
Choose 1 answer:
A)
(4pi)/(3) radians
(B)
(5pi)/(3) radians
(C)
(7pi)/(3) radians
(D)
(11 pi)/(3) radians

Which of the following radian measures is equal to $240^{\circ}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{4 \pi}{3}$ radians $\newline$ B $\frac{5 \pi}{3}$ radians $\newline$ (C) $\frac{7 \pi}{3}$ radians $\newline$ (D) $\frac{11 \pi}{3}$ radians

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Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

240^{\circ}

?

\newline

Choose

1

answer:

\newline

(A)

\frac{4 \pi}{3}

radians

\newline

B

\frac{5 \pi}{3}

radians

\newline

(C)

\frac{7 \pi}{3}

radians

\newline

(D)

\frac{11 \pi}{3}

radians

Identify formula for conversion: Identify the formula to convert degrees to radians. The formula is $\text{radians} = \text{degrees} \times \left(\frac{\pi}{180^\circ}\right)$ .
Convert $240$ degrees to radians: Convert $240$ degrees into radians using the formula. By substituting $240$ degrees into the formula, we get $240^\circ \times \left(\frac{\pi}{180^\circ}\right) = \left(\frac{240}{180}\right) \times \pi = \left(\frac{4}{3}\right) \times \pi$ radians.
Simplify fraction $(\frac{4}{3})$ : Simplify the fraction $(\frac{4}{3})$ to find the exact radian measure. $(\frac{4}{3}) \times \pi$ radians simplifies to $(\frac{4\pi}{3})$ radians.
Match radian measure with options: Match the calculated radian measure with the given options. The correct option that matches $(4\pi/3)$ radians is option A.

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