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Which of the following radian measures is equal to 540^(@) ? (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) 9pi radians (D) 12 pi radians

Which of the following radian measures is equal to 540∘ 540^{\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) 9π 9 \pi radians\newline(D) 12π 12 \pi radians

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Full solution

Q. Which of the following radian measures is equal to 540∘ 540^{\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) 9π 9 \pi radians\newline(D) 12π 12 \pi radians
  1. Identify conversion formula: Identify the conversion formula from degrees to radians. The formula to convert degrees to radians is radians=degrees×(π180°)\text{radians} = \text{degrees} \times \left(\frac{\pi}{180°}\right).
  2. Convert 540540 degrees: Convert 540540 degrees into radians using the formula. By substituting 540540 degrees into the formula, we get 540∘×(π/180∘)=3×π540^\circ \times (\pi/180^\circ) = 3 \times \pi radians.
  3. Perform calculation: Perform the calculation to find the exact radian measure. 540°×(π/180°)=3×π=3π540° \times (\pi/180°) = 3 \times \pi = 3\pi radians.
  4. Choose correct option: Choose the correct option of radians for 540°540°. The correct option is 3π3\pi radians, which is equivalent to 540°540°.

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