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Which of the following radian measures is equal to 45^(@) ? Choose 1 answer: A) (pi)/(2) radians (B) (pi)/(3) radians (c) (pi)/(4) radians (D) (pi)/(6) radians

Which of the following radian measures is equal to 45∘ 45^{\circ} ?\newlineChoose 11 answer:\newline(A) π2 \frac{\pi}{2} radians\newlineB 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\newlineB π3 \frac{\pi}{3} radians\newline(C) π4 \frac{\pi}{4} radians\newline(D) π6 \frac{\pi}{6} radians
  1. Convert to Radians: To convert degrees to radians, we use the conversion factor that 180180 degrees is equal to π\pi radians. Therefore, to find the radian measure equivalent to 4545 degrees, we set up the proportion: (45 degrees)×(π radians/180 degrees)(45 \text{ degrees}) \times (\pi \text{ radians} / 180 \text{ degrees}).
  2. Calculate Value: Now we calculate the value: (45/180)×π=(1/4)×π=π/4(45/180) \times \pi = (1/4) \times \pi = \pi/4 radians.
  3. Check Calculation: We check our calculation to ensure that we have not made any errors in the conversion process. Since 4545 is one-fourth of 180180, it is correct that 4545 degrees is equal to π/4\pi/4 radians.

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