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The questions below are posed in order to help you think about how to find the number of degrees in (5pi)/(6) radians. What fraction of a semicircle is an angle that measures (5pi)/(6) radians? Express your answer as a fraction in simplest terms.

The questions below are posed in order to help you think about how to find the number of degrees in 5π6 \frac{5 \pi}{6} radians.\newlineWhat fraction of a semicircle is an angle that measures 5π6 \frac{5 \pi}{6} radians? Express your answer as a fraction in simplest terms.

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Full solution

Q. The questions below are posed in order to help you think about how to find the number of degrees in 5π6 \frac{5 \pi}{6} radians.\newlineWhat fraction of a semicircle is an angle that measures 5π6 \frac{5 \pi}{6} radians? Express your answer as a fraction in simplest terms.
  1. Total Radians in Semicircle: To determine what fraction of a semicircle an angle represents, we need to know the total radians in a semicircle. A semicircle is half of a circle, and a full circle is 2π2\pi radians. Therefore, a semicircle is π\pi radians.
  2. Express Angle as Fraction: Now, we can express the given angle (5π/6)(5\pi/6) as a fraction of a semicircle by dividing it by π\pi, the total radians in a semicircle.\newlineSo, the fraction is (5π/6)/π(5\pi/6) / \pi.
  3. Simplify the Fraction: To simplify the fraction, we divide the numerator by the denominator. Since π\pi is in both the numerator and the denominator, they cancel each other out.\newlineThis leaves us with 56\frac{5}{6}.

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