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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)/(12) radians. What fraction of a semicircle is an angle that measures (5pi)/(12) 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 5π12 \frac{5 \pi}{12} radians.\newlineWhat fraction of a semicircle is an angle that measures 5π12 \frac{5 \pi}{12} 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 5π12 \frac{5 \pi}{12} radians.\newlineWhat fraction of a semicircle is an angle that measures 5π12 \frac{5 \pi}{12} radians? Express your answer as a fraction in simplest terms.
  1. Total Radians in Semicircle: To find the fraction of a semicircle that an angle of (5π)/(12)(5\pi)/(12) radians 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. Calculate Fraction: Now, we divide the angle in question, (5π)/(12)(5\pi)/(12) radians, by the total radians in a semicircle, which is π\pi radians. This will give us the fraction of the semicircle that the angle represents.\newlineCalculation: (5π)/(12)÷π=5/12(5\pi)/(12) \div \pi = 5/12
  3. Check Simplified Form: We should check that the fraction is in its simplest form. Since 55 and 1212 have no common factors other than 11, the fraction 512\frac{5}{12} is already in simplest form.

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