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Which of the following radian measures is equal to
1,080^(@) ?
(The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is
2pi.)

Which of the following radian measures is equal to $1,080^{\circ}$ ? $\newline$ (The number of degrees of arc in a circle is $360$ . The number of radians of arc in a circle is $2 \pi$ .)

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Reflections of functions

Full solution

Q. Which of the following radian measures is equal to

1,080^{\circ}

?

\newline

(The number of degrees of arc in a circle is

360

. The number of radians of arc in a circle is

2 \pi

.)

Set up proportion: To convert degrees to radians, we use the fact that $360$ degrees is equal to $2\pi$ radians. Therefore, we can set up a proportion to find the radian measure equivalent to $1,080$ degrees.
Cross-multiply: First, we write the proportion using the known conversion: $360$ degrees $= 2\pi$ radians. Then we set up the proportion as follows: $(1,080 \text{ degrees} / 360 \text{ degrees}) = (x \text{ radians} / 2\pi \text{ radians})$ .
Isolate x: Next, we solve for x by cross-multiplying: $1,080$ degrees $\times 2\pi$ radians = $x$ radians $\times 360$ degrees.
Simplify equation: Now we divide both sides of the equation by $360$ degrees to isolate $x$ : $x = (1,080 \times 2\pi) / 360$ .
Simplify equation: Now we divide both sides of the equation by $360$ degrees to isolate $x$ : $x = (1,080 \times 2\pi) / 360$ . Simplifying the right side of the equation, we get: $x = (1,080 / 360) \times 2\pi = 3 \times 2\pi = 6\pi$ .

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