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Which of the following degree measures is equal to 3pi radians? (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) 60^(@) (B) 120^(@) (c) 180^(@) (D) 540^(@)

Which of the following degree measures is equal to 3π 3 \pi radians?\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) 60∘ 60^{\circ} \newline(B) 120∘ 120^{\circ} \newline(C) 180∘ 180^{\circ} \newline(D) 540∘ 540^{\circ}

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Full solution

Q. Which of the following degree measures is equal to 3π 3 \pi radians?\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) 60∘ 60^{\circ} \newline(B) 120∘ 120^{\circ} \newline(C) 180∘ 180^{\circ} \newline(D) 540∘ 540^{\circ}
  1. Identify relationship between degrees and radians: Identify the relationship between degrees and radians. We know that 2π2\pi radians is equal to 360360 degrees. This relationship can be used to convert radians to degrees.
  2. Set up conversion from radians to degrees: Set up the conversion from radians to degrees. To convert 3π3\pi radians to degrees, we use the proportion:\newline3π radians2π radians=x degrees360 degrees\frac{3\pi \text{ radians}}{2\pi \text{ radians}} = \frac{x \text{ degrees}}{360 \text{ degrees}}
  3. Solve for degree measure: Solve for xx, which represents the degree measure. Cross-multiply to find the value of xx:3π×360=2π×x3\pi \times 360 = 2\pi \times x
  4. Isolate x: Divide both sides of the equation by 2π2\pi to isolate xx: (3π×3602π)=x\left(\frac{3\pi \times 360}{2\pi}\right) = x
  5. Calculate value of x: Calculate the value of xx:
    x=(3×360)/2x = (3 \times 360) / 2
    x=1080/2x = 1080 / 2
    x=540x = 540
  6. Choose correct option of degrees: Choose the correct option of degrees for 3π3\pi radians. The correct option is 540540 degrees, which is equivalent to 3π3\pi radians.

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