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If
a pi radians is equal to 1,440 degrees, what is the value of
a ?
(The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is
2pi.)

If $a \pi$ radians is equal to $1$ , $440$ degrees, what is the value of $a$ ? $\newline$ (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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Convert between radians and degrees

Full solution

Q. If

a \pi

radians is equal to

1

,

440

degrees, what is the value of

a

?

\newline

(The number of degrees of arc in a circle is

360

. The number of radians of arc in a circle is

2 \pi

.)

Convert units using proportion: We know that $2\pi$ radians is equal to $360$ degrees. Therefore, we can set up a proportion to find the value of $a$ when $a \pi$ radians is equal to $1,440$ degrees.
Set up proportion: Set up the proportion using the relationship between radians and degrees: $\newline$ $a \pi \text{ radians} = 1440 \text{ degrees}$ $\newline$ $2\pi \text{ radians} = 360 \text{ degrees}$
Simplify proportion: To find the value of a, we can write the proportion as: $\newline$ $\frac{a \pi}{2\pi} = \frac{1440}{360}$
Divide to simplify: Simplify the proportion by dividing both sides by pi: $\newline$ $\frac{a}{2} = \frac{1440}{360}$
Multiply to solve: Now, divide $1440$ by $360$ to simplify the right side of the equation: $\newline$ $\frac{a}{2} = 4$
Calculate value: To find the value of a, multiply both sides of the equation by $2$ : $\newline$ $a = 4 \times 2$
Calculate value: To find the value of a, multiply both sides of the equation by $2$ : $\newline$ $a = 4 \times 2$ Calculate the value of a: $\newline$ $a = 8$

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