Which of the following radian measures is equal to 165^(@) ? Choose 1 answer: (A) (5pi)/(12) radians (B) (7pi)/(12) radians (C) (5pi)/(6) radians (D) (11 pi)/(12) radians

Identify Formula: Identify the formula to convert degrees to radians. The formula to convert degrees to radians is radians = degrees × (π/180°).Convert Degrees to Radians: Convert 165 degrees into radians using the formula. 165° = 165 × (π/180°) = (165/180) × π = (11/12) × π = (11π)/12 radians.Match Result: Match the result with the given options. The calculation shows that 165 degrees is equal to (11π)/12 radians. Therefore, the correct option is (D) (11π)/12 radians.

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Which of the following radian measures is equal to
165^(@) ?
Choose 1 answer:
(A)
(5pi)/(12) radians
(B)
(7pi)/(12) radians
(C)
(5pi)/(6) radians
(D)
(11 pi)/(12) radians

Which of the following radian measures is equal to $165^{\circ}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{5\pi}{12}$ radians $\newline$ (B) $\frac{7\pi}{12}$ radians $\newline$ (C) $\frac{5\pi}{6}$ radians $\newline$ (D) $\frac{11\pi}{12}$ radians

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Math Problems

Algebra 2

Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

165^{\circ}

\newline

Choose

1

answer:

\newline

(A)

\frac{5\pi}{12}

radians

\newline

(B)

\frac{7\pi}{12}

radians

\newline

(C)

\frac{5\pi}{6}

radians

\newline

(D)

\frac{11\pi}{12}

radians

Identify Formula: Identify the formula to convert degrees to radians. $\newline$ The formula to convert degrees to radians is $\text{radians} = \text{degrees} \times \left(\frac{\pi}{180°}\right)$ .
Convert Degrees to Radians: Convert $165$ degrees into radians using the formula. $\newline$ $165^\circ = 165 \times (\pi/180^\circ) = (165/180) \times \pi = (11/12) \times \pi = (11\pi)/12$ radians.
Match Result: Match the result with the given options. $\newline$ The calculation shows that $165$ degrees is equal to $(11\pi)/12$ radians. Therefore, the correct option is (D) $(11\pi)/12$ radians.