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Which of the following degree measures is equal to
5pi radians?
(The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is
2pi.)
Choose 1 answer:
(A)
144^(@)
(B)
900^(@)
(C)
1,080^(@)
(D)
1,800^(@)

Which of the following degree measures is equal to $5 \pi$ radians? $\newline$ (The number of degrees of arc in a circle is $360$ . The number of radians of arc in a circle is $2 \pi$ .) $\newline$ Choose $1$ answer: $\newline$ (A) $144^{\circ}$ $\newline$ (B) $900^{\circ}$ $\newline$ (C) $1,080^{\circ}$ $\newline$ (D) $1,800^{\circ}$

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. Which of the following degree measures is equal to

5 \pi

radians?

\newline

(The number of degrees of arc in a circle is

360

. The number of radians of arc in a circle is

2 \pi

.)

\newline

Choose

1

answer:

\newline

(A)

144^{\circ}

\newline

(B)

900^{\circ}

\newline

(C)

1,080^{\circ}

\newline

(D)

1,800^{\circ}

Conversion Factor Proportion: To convert radians to degrees, we use the conversion factor that $2\pi$ radians is equal to $360$ degrees. We can set up a proportion to find the equivalent degree measure for $5\pi$ radians.
Calculation: Using the proportion, we have $(5\pi \text{ radians}) \times (360 \text{ degrees} / 2\pi \text{ radians})$ . The $\pi$ units cancel out, and we are left with the calculation $5 \times (360 / 2)$ .
Final Result: Performing the calculation, we get $5 \times 180$ , which equals $900$ .
Matching Result: Therefore, $5\pi$ radians is equal to $900$ degrees. We can now match this result with the given choices.

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