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Which of the following radian measures is equal to 1,080^(@) ? (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 3pi radians (B) 6pi radians (C) 10 pi radians (D) 12 pi radians

Which of the following radian measures is equal to 1,080∘ 1,080^{\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) 3π 3 \pi radians\newline(B) 6π 6 \pi radians\newline(C) 10π 10 \pi radians\newline(D) 12π 12 \pi radians

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Full solution

Q. Which of the following radian measures is equal to 1,080∘ 1,080^{\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) 3π 3 \pi radians\newline(B) 6π 6 \pi radians\newline(C) 10π 10 \pi radians\newline(D) 12π 12 \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, or π180\frac{\pi}{180} radians.
  2. Converting degrees to radians: Convert 1,0801,080 degrees to radians using the relationship from Step 11. Multiply 1,0801,080 degrees by π180\frac{\pi}{180} to find the equivalent in radians.\newlineCalculation: 1,080×(π180)=6×π1,080 \times \left(\frac{\pi}{180}\right) = 6 \times \pi
  3. Simplifying the calculation: Simplify the calculation to find the final answer. 1,080×(π/180)1,080 \times (\pi/180) simplifies to 6π6\pi because 1,0801,080 divided by 180180 equals 66.\newlineCalculation: 6×π=6π6 \times \pi = 6\pi radians
  4. Choosing the correct option: Choose the correct option from the given choices that matches the calculated radian measure.\newlineThe correct option is (B) 6π6\pi radians.

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