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Which of the following radian measures is equal to 2,880^(@) ? (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 4pi radians (B) 8pi radians (C) 12 pi radians (D) 16 pi radians

Which of the following radian measures is equal to 2,880∘ 2,880^{\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) 4π 4 \pi radians\newline(B) 8π 8 \pi radians\newline(C) 12π 12 \pi radians\newline(D) 16π 16 \pi radians

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Full solution

Q. Which of the following radian measures is equal to 2,880∘ 2,880^{\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) 4π 4 \pi radians\newline(B) 8π 8 \pi radians\newline(C) 12π 12 \pi radians\newline(D) 16π 16 \pi radians
  1. Understand Relationship: 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. Convert Degrees to Radians: Convert 2,8802,880 degrees to radians. Using the conversion factor from Step 11, we multiply 2,8802,880 degrees by π/180\pi/180 radians/degree to find the equivalent in radians.\newline2,8802,880 degrees ×(π/180\times (\pi/180 radians/degree) =(2,880/180)×π= (2,880/180) \times \pi radians =16×π= 16 \times \pi radians.
  3. Choose Correct Option: Choose the correct option that matches our calculation. The correct option is 16π16\pi radians, which is equivalent to 2,8802,880 degrees.

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