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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 for conversion: Identify the formula to convert degrees to radians. The formula is radians=degrees×(π180∘)\text{radians} = \text{degrees} \times \left(\frac{\pi}{180^\circ}\right).
  2. Convert 165165 degrees to radians: Convert 165165 degrees into radians using the formula. By substituting 165165 degrees into the formula, we get 165∘×(π180∘)=(165180)×π=(1112)×π165^\circ \times \left(\frac{\pi}{180^\circ}\right) = \left(\frac{165}{180}\right) \times \pi = \left(\frac{11}{12}\right) \times \pi radians.
  3. Simplify fraction (1112)(\frac{11}{12}): Simplify the fraction (1112)(\frac{11}{12}) if necessary. In this case, the fraction is already in its simplest form, so no further simplification is needed.
  4. Choose correct option for 165165 degrees: Choose the correct option of radians for 165165 degrees. The correct option is (11π12)(\frac{11\pi}{12}) radians, which is equivalent to 165165 degrees.

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