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The questions below are posed in order to help you think about how to find the number of degrees in (25 pi)/(18) radians. What fraction of a semicircle is an angle that measures (25 pi)/(18) 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 25π18 \frac{25 \pi}{18} radians.\newlineWhat fraction of a semicircle is an angle that measures 25π18 \frac{25 \pi}{18} 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 25π18 \frac{25 \pi}{18} radians.\newlineWhat fraction of a semicircle is an angle that measures 25π18 \frac{25 \pi}{18} radians? Express your answer as a fraction in simplest terms.
  1. Identify Semicircle Measure: To find the fraction of a semicircle that an angle of (25π)/(18)(25 \pi)/(18) radians represents, we need to know the radian measure of 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 as a fraction of π\pi radians. To do this, we divide the angle in radians by π\pi radians to find the fraction of a semicircle it represents.\newlineSo, the fraction is 25π18/π\frac{25 \pi}{18} / \pi.
  3. Simplify Fraction: Simplify the fraction by canceling out the π\pi in the numerator and the π\pi in the denominator. This leaves us with 2518\frac{25}{18}.
  4. Final Fraction: The fraction 2518\frac{25}{18} is already in its simplest form, as 2525 and 1818 have no common factors other than 11.

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