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Which of the following radian measures is equal to \newline165∘165^\circ?\newlineChoose 11 answer:\newline(A) \newline5π12\frac{5\pi}{12} radians\newline(B) \newline7π12\frac{7\pi}{12} radians\newline(C) \newline5π6\frac{5\pi}{6} radians\newline(D) \newline11π12\frac{11\pi}{12} radians

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Full solution

Q. Which of the following radian measures is equal to \newline165∘165^\circ?\newlineChoose 11 answer:\newline(A) \newline5π12\frac{5\pi}{12} radians\newline(B) \newline7π12\frac{7\pi}{12} radians\newline(C) \newline5π6\frac{5\pi}{6} radians\newline(D) \newline11π12\frac{11\pi}{12} radians
  1. Identify Formula: Identify the formula to convert degrees to radians. The formula 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. By substituting 165165 degrees into the formula, we get 165∘×(π/180∘)=(165π/180)165^\circ \times (\pi/180^\circ) = (165\pi/180) radians.
  3. Simplify Fraction: Simplify the fraction (165π/180)(165\pi/180) to its lowest terms. Both the numerator and the denominator are divisible by 1515. Dividing both by 1515, we get (11π/12)(11\pi/12) radians.
  4. Match to Choices: Match the simplified radian measure to the given choices. The correct match from the choices is (D)(11π12)(D) \left(\frac{11\pi}{12}\right) radians.

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