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$The questions below are posed in order to help you think about how to find the number of degrees in (7pi)/(9) radians. What fraction of a semicircle is an angle that measures (7pi)/(9) radians? Express your answer as a fraction in simplest terms.$

The questions below are posed in order to help you think about how to find the number of degrees in $\frac{7 \pi}{9}$ radians. $\newline$ What fraction of a semicircle is an angle that measures $\frac{7 \pi}{9}$ radians? Express your answer as a fraction in simplest terms.

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Precalculus

Inverses of trigonometric functions

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Q. The questions below are posed in order to help you think about how to find the number of degrees in

\frac{7 \pi}{9}

radians.

\newline

What fraction of a semicircle is an angle that measures

\frac{7 \pi}{9}

radians? Express your answer as a fraction in simplest terms.

Identify Semicircle Radians: To find the fraction of a semicircle that an angle of $(7\pi)/(9)$ radians represents, we need to compare it to the total radians in a semicircle. $\newline$ A semicircle is half of a circle, and a full circle is $2\pi$ radians. Therefore, a semicircle is $\pi$ radians.
Express Angle as Fraction: Now, we express $(7\pi)/(9)$ as a fraction of $\pi$ to find out what fraction of a semicircle it is. $\newline$ We can write $(7\pi)/(9)$ as $(7/9) \times \pi$ .
Calculate Fraction of Semicircle: To find the fraction of a semicircle, we divide $(7\pi)/(9)$ by $\pi$ , which is the radian measure of a semicircle. $\newline$ So, the fraction is $(7\pi)/(9) / \pi = (7/9) \times (\pi/\pi) = 7/9$ .
Simplify Fraction: We simplify the fraction by canceling out the $\pi$ terms in the numerator and the denominator. $\newline$ This leaves us with the fraction $\frac{7}{9}$ , which is already in its simplest form.