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Which of the following radian measures is equal to 45∘45^{\circ} ?\newlineChoose 11 answer:\newline(A) π2\frac{\pi}{2} radians\newline(B) π3\frac{\pi}{3} radians\newline(C) π4\frac{\pi}{4} radians\newline(D) π6\frac{\pi}{6} radians

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Full solution

Q. Which of the following radian measures is equal to 45∘45^{\circ} ?\newlineChoose 11 answer:\newline(A) π2\frac{\pi}{2} radians\newline(B) π3\frac{\pi}{3} radians\newline(C) π4\frac{\pi}{4} radians\newline(D) π6\frac{\pi}{6} 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^\circ}\right).
  2. Convert degrees to radians: Convert 4545 degrees into radians using the formula. By substituting 4545 degrees into the formula, we get 45∘×(π/180∘)=π/445^\circ \times (\pi/180^\circ) = \pi/4 radians.
  3. Match with options: Match the result with the given options. The correct option that represents π4\frac{\pi}{4} radians is (C) (π4)\left(\frac{\pi}{4}\right) radians.

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