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Which of the following radian measures is equal to 300^(@) ? Choose 1 answer: A) (2pi)/(3) radians (B) (4pi)/(3) radians (C) (5pi)/(3) radians (D) (7pi)/(3) radians

Which of the following radian measures is equal to 300∘ 300^{\circ} ?\newlineChoose 11 answer:\newline(A) 2π3 \frac{2 \pi}{3} radians\newlineB 4π3 \frac{4 \pi}{3} radians\newline(C) 5π3 \frac{5 \pi}{3} radians\newline(D) 7π3 \frac{7 \pi}{3} radians

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Full solution

Q. Which of the following radian measures is equal to 300∘ 300^{\circ} ?\newlineChoose 11 answer:\newline(A) 2π3 \frac{2 \pi}{3} radians\newlineB 4π3 \frac{4 \pi}{3} radians\newline(C) 5π3 \frac{5 \pi}{3} radians\newline(D) 7π3 \frac{7 \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 300300 degrees to radians: Convert 300300 degrees into radians using the formula. By substituting 300300 degrees into the formula, we get 300∘×(π/180∘)=(300/180)×π=(5/3)×π300^\circ \times (\pi/180^\circ) = (300/180) \times \pi = (5/3) \times \pi radians.
  3. Simplify fraction to find radian measure: Simplify the fraction (53)×π(\frac{5}{3}) \times \pi to find the radian measure. The simplified form is (5π3)(\frac{5\pi}{3}) radians.
  4. Choose correct option for 300300 degrees: Choose the correct option of radians for 300300 degrees. The correct option is rac{5oldsymbol{ ext{ extpi}}}{3} radians, which is equivalent to 300300 degrees.

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