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Which of the following radian measures is equal to 225^(@) ? Choose 1 answer: A) (pi)/(4) radians (B) (pi)/(2) radians (C) (3pi)/(4) radians (D) (5pi)/(4) radians

Which of the following radian measures is equal to 225∘ 225^{\circ} ?\newlineChoose 11 answer:\newline(A) π4 \frac{\pi}{4} radians\newlineB π2 \frac{\pi}{2} radians\newline(C) 3π4 \frac{3 \pi}{4} radians\newline(D) 5π4 \frac{5 \pi}{4} radians

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Full solution

Q. Which of the following radian measures is equal to 225∘ 225^{\circ} ?\newlineChoose 11 answer:\newline(A) π4 \frac{\pi}{4} radians\newlineB π2 \frac{\pi}{2} radians\newline(C) 3π4 \frac{3 \pi}{4} radians\newline(D) 5π4 \frac{5 \pi}{4} 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 225225 degrees to radians: Convert 225225 degrees into radians using the formula. By substituting 225225 degrees into the formula, we get 225∘×(π180∘)=(225180)×π=(54)×π=5π4225^\circ \times \left(\frac{\pi}{180^\circ}\right) = \left(\frac{225}{180}\right) \times \pi = \left(\frac{5}{4}\right) \times \pi = \frac{5\pi}{4} radians.
  3. Match calculated radian measure: Match the calculated radian measure with the given options. The calculated value is (5π/4)(5\pi/4) radians, which corresponds to option (D).

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