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Which of the following radian measures is equal to 90∘90^{\circ}? \newlineChoose 11 answer: \newline(A) π3\frac{\pi}{3} radians \newline(B) π4\frac{\pi}{4} radians \newline(C) π2\frac{\pi}{2} radians \newline(D) π6\frac{\pi}{6} radians

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Full solution

Q. Which of the following radian measures is equal to 90∘90^{\circ}? \newlineChoose 11 answer: \newline(A) π3\frac{\pi}{3} radians \newline(B) π4\frac{\pi}{4} radians \newline(C) π2\frac{\pi}{2} radians \newline(D) π6\frac{\pi}{6} radians
  1. Identify Conversion Formula: Identify the conversion formula from degrees to radians.\newlineThe formula to convert degrees to radians is radians=degrees×(π180°)\text{radians} = \text{degrees} \times \left(\frac{\pi}{180°}\right).
  2. Apply Formula to 9090 Degrees: Apply the conversion formula to 9090 degrees.\newlineUsing the formula, we convert 9090 degrees to radians: 90∘×(π/180∘)=π/290^\circ \times (\pi/180^\circ) = \pi/2 radians.
  3. Match Result with Options: Match the result with the given options.\newlineThe calculation from Step 22 shows that 9090 degrees is equal to π/2\pi/2 radians. Therefore, the correct answer from the given options is (C) π/2\pi/2 radians.

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