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Which of the following radian measures is equal to 75^(@) ? Choose 1 answer: (A) (pi)/(12) radians (B) (pi)/(3) radians (C) (5pi)/(12) radians (D) (7pi)/(12) radians

Which of the following radian measures is equal to 75∘75^{\circ}? \newlineChoose 11 answer: \newline(A) π12\frac{\pi}{12} radians \newline(B) π3\frac{\pi}{3} radians \newline(C) 5π12\frac{5\pi}{12} radians \newline(D) 7π12\frac{7\pi}{12} radians

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Full solution

Q. Which of the following radian measures is equal to 75∘75^{\circ}? \newlineChoose 11 answer: \newline(A) π12\frac{\pi}{12} radians \newline(B) π3\frac{\pi}{3} radians \newline(C) 5π12\frac{5\pi}{12} radians \newline(D) 7π12\frac{7\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 7575 degrees to radians using the formula. By substituting 7575 degrees into the formula, we get 75∘×(π/180∘)=(75/180)×π=(5/12)×π75^\circ \times (\pi/180^\circ) = (75/180) \times \pi = (5/12) \times \pi radians.
  3. Simplify Fraction: Simplify the fraction (512)⋅π(\frac{5}{12}) \cdot \pi to find the radian measure. The fraction is already in its simplest form, so the radian measure is (5π12)(\frac{5\pi}{12}) radians.
  4. Choose Correct Option: Choose the correct option of radians for 7575 degrees. The correct option is 5π12\frac{5\pi}{12} radians, which is equivalent to 7575 degrees.

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