Question
If x degrees is equal to 7 pi radians, what is the value of x?
(The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2 pi)
(The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2 pi)
Answers
Answered by
GPT-4o mini
To convert radians to degrees, we can use the conversion factor that \(180\) degrees is equal to \(\pi\) radians.
Given that \(x\) degrees is equal to \(7\pi\) radians, we set up the following equation:
\[
x = 7\pi \times \frac{180}{\pi}
\]
In this equation, the \(\pi\) in the numerator and the \(\pi\) in the denominator will cancel out:
\[
x = 7 \times 180
\]
Now, we multiply:
\[
x = 1260
\]
Therefore, the value of \(x\) is:
\[
\boxed{1260}
\] degrees.
Given that \(x\) degrees is equal to \(7\pi\) radians, we set up the following equation:
\[
x = 7\pi \times \frac{180}{\pi}
\]
In this equation, the \(\pi\) in the numerator and the \(\pi\) in the denominator will cancel out:
\[
x = 7 \times 180
\]
Now, we multiply:
\[
x = 1260
\]
Therefore, the value of \(x\) is:
\[
\boxed{1260}
\] degrees.