An arc subtends a central angle measuring $\frac{7 \pi}{4}$ radians.

What fraction of the circumference is this arc?
$\square$ of the circumference

Question

An arc subtends a central angle measuring $\frac{7 \pi}{4}$ radians.

What fraction of the circumference is this arc?
$\square$ of the circumference

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the fraction of the circumference that the arc subtends, we need to compare the angle of the arc to the full angle of a circle in radians. ‖ ‖ step 2 ⋮ The full angle of a circle in radians is $2\pi$. ‖ ‖ step 3 ⋮ The angle of the arc given is $\frac{7\pi}{4}$. ‖ ‖ step 4 ⋮ To find the fraction of the circumference, divide the angle of the arc by the full angle of a circle: $\frac{\frac{7\pi}{4}}{2\pi}$. ‖ ‖ step 5 ⋮ Simplify the fraction: $\frac{7\pi}{4} \div 2\pi = \frac{7}{8}$. ‖ ∻Answer∻ ⚹ $\frac{7}{8}$ of the circumference ⚹ ∻Key Concept∻ ⚹Fraction of Circumference⚹ ∻Explanation∻ ⚹The fraction of the circumference represented by an arc is the ratio of the arc's central angle to the full angle of a circle in radians.⚹◊What is the formula to calculate the fraction of the circumference represented by an arc subtending a central angle in radians?⍭ Generate me a similar question◊

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