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Which of the following radian measures is equal to 2,8802,880^{\circ} ?\newline(The number of degrees of arc in a circle is 360360^{\circ} . The number of radians of arc in a circle is 2π2\pi.)\newlineChoose 11 answer:\newline(A) 4π4\pi radians\newline(B) 8π8\pi radians\newline(C) 12π12\pi radians\newline(D) 16π16\pi radians

Full solution

Q. Which of the following radian measures is equal to 2,8802,880^{\circ} ?\newline(The number of degrees of arc in a circle is 360360^{\circ} . The number of radians of arc in a circle is 2π2\pi.)\newlineChoose 11 answer:\newline(A) 4π4\pi radians\newline(B) 8π8\pi radians\newline(C) 12π12\pi radians\newline(D) 16π16\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 relationship from Step 11. Multiply 2,8802,880 degrees by π/180\pi/180 to find the equivalent in radians.\newline2,8802,880 degrees π/180=(2,880/180)π=16π* \pi/180 = (2,880/180) * \pi = 16 * \pi radians.
  3. Check Answer Choices: Check the answer choices to see which one matches our calculation. The correct answer is 16×π16 \times \pi radians.

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