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Which of the following radian measures is equal to 120^(@) ? Choose 1 answer: (A) (2pi)/(3) radians (B) pi radians (C) (4pi)/(3) radians (D) (5pi)/(3) radians

Which of the following radian measures is equal to 120∘ 120^{\circ} ?\newlineChoose 11 answer:\newline(A) 2π3 \frac{2 \pi}{3} radians\newline(B) π \pi radians\newline(C) 4π3 \frac{4 \pi}{3} radians\newline(D) 5π3 \frac{5 \pi}{3} radians

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Full solution

Q. Which of the following radian measures is equal to 120∘ 120^{\circ} ?\newlineChoose 11 answer:\newline(A) 2π3 \frac{2 \pi}{3} radians\newline(B) π \pi radians\newline(C) 4π3 \frac{4 \pi}{3} radians\newline(D) 5π3 \frac{5 \pi}{3} 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 120120 degrees to radians: Convert 120120 degrees into radians using the formula. By substituting 120120 degrees into the formula, we get 120∘×(π180∘)=(120180)×π=(23)×π120^\circ \times \left(\frac{\pi}{180^\circ}\right) = \left(\frac{120}{180}\right) \times \pi = \left(\frac{2}{3}\right) \times \pi.
  3. Simplify fraction to find radian measure: Simplify the fraction (23)⋅π(\frac{2}{3}) \cdot \pi to find the radian measure. (23)⋅π=2π3(\frac{2}{3}) \cdot \pi = \frac{2\pi}{3} radians.
  4. Match result with given options: Match the result with the given options. The correct option that matches (2π)/3(2\pi)/3 radians is (A) (2π)/(3)(2\pi)/(3) radians.

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