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Which of the following radian measures is equal to 150^(@) ? Choose 1 answer: (A) (pi)/(3) radians (B) (pi)/(2) radians (C) (2pi)/(3) radians (D) (5pi)/(6) radians

Which of the following radian measures is equal to 150∘ 150^{\circ} ?\newlineChoose 11 answer:\newline(A) π3 \frac{\pi}{3} radians\newline(B) π2 \frac{\pi}{2} radians\newline(C) 2π3 \frac{2 \pi}{3} radians\newline(D) 5π6 \frac{5 \pi}{6} radians

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Full solution

Q. Which of the following radian measures is equal to 150∘ 150^{\circ} ?\newlineChoose 11 answer:\newline(A) π3 \frac{\pi}{3} radians\newline(B) π2 \frac{\pi}{2} radians\newline(C) 2π3 \frac{2 \pi}{3} radians\newline(D) 5π6 \frac{5 \pi}{6} radians
  1. Convert to radians: We need to convert degrees to radians using the formula radians=degrees×(π/180)\text{radians} = \text{degrees} \times (\pi/180).
  2. Plug in degrees: Now, plug in 150150 degrees into the formula: radians=150×(π/180)\text{radians} = 150 \times (\pi/180).
  3. Simplify fraction: Simplify the fraction: radians = (150180)×π=(56)×π(\frac{150}{180}) \times \pi = (\frac{5}{6}) \times \pi.
  4. Final conversion: So, 150150 degrees is equal to (5π/6)(5\pi/6) radians.

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