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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∘165^{\circ}? \newlineChoose 11 answer:\newline(A) 5π12\frac{5\pi}{12} radians\newline(B) 7π12\frac{7\pi}{12} radians\newline(C) 5π6\frac{5\pi}{6} radians\newline(D) 11π12\frac{11\pi}{12} radians

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Full solution

Q. Which of the following radian measures is equal to 165∘165^{\circ}? \newlineChoose 11 answer:\newline(A) 5π12\frac{5\pi}{12} radians\newline(B) 7π12\frac{7\pi}{12} radians\newline(C) 5π6\frac{5\pi}{6} radians\newline(D) 11π12\frac{11\pi}{12} radians
  1. Identify Formula: Identify the formula to convert degrees to radians.\newlineThe formula to convert degrees to radians is radians=degrees×(π180°)\text{radians} = \text{degrees} \times \left(\frac{\pi}{180°}\right).
  2. Convert Degrees to Radians: Convert 165165 degrees into radians using the formula.\newline165∘=165×(π/180∘)=(165/180)×π=(11/12)×π=(11π)/12165^\circ = 165 \times (\pi/180^\circ) = (165/180) \times \pi = (11/12) \times \pi = (11\pi)/12 radians.
  3. Match Result: Match the result with the given options.\newlineThe calculation shows that 165165 degrees is equal to (11π)/12(11\pi)/12 radians. Therefore, the correct option is (D) (11π)/12(11\pi)/12 radians.

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