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Which of the following radian measures is equal to 720^(@) ? (The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is 2pi.) Choose 1 answer: A pi radians (B) 2pi radians (c) 4pi radians (D) 8pi radians

Which of the following radian measures is equal to 720∘ 720^{\circ} ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)\newlineChoose 11 answer:\newline(A) π \pi radians\newline(B) 2π 2 \pi radians\newline(C) 4π 4 \pi radians\newline(D) 8π 8 \pi radians

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Full solution

Q. Which of the following radian measures is equal to 720∘ 720^{\circ} ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)\newlineChoose 11 answer:\newline(A) π \pi radians\newline(B) 2π 2 \pi radians\newline(C) 4π 4 \pi radians\newline(D) 8π 8 \pi radians
  1. Understanding degrees and radians: Understand the relationship between degrees and radians. We know that 360360 degrees is equal to 2π2\pi radians. This means that 11 degree is equal to 2π360\frac{2\pi}{360} radians, which simplifies to π180\frac{\pi}{180} radians.
  2. Converting 720720 degrees to radians: Convert 720720 degrees into radians using the relationship from Step 11. Multiply 720720 degrees by the conversion factor π180\frac{\pi}{180} radians per degree.\newlineCalculation: 720720 degrees ×(π180 radians/degree)=4π\times \left(\frac{\pi}{180} \text{ radians/degree}\right) = 4\pi radians.
  3. Determining the radians for 720720 degrees: Choose the correct option of radians for 720720 degrees. According to the calculation in Step 22, 720720 degrees is equal to 4π4\pi radians.

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