To convert an angle from radians to degrees, we need to use the conversion factor between radians and degrees. One complete circle is [tex]\( 2\pi \)[/tex] radians, which is equivalent to [tex]\( 360^{\circ} \)[/tex] (degrees). Therefore, [tex]\( \pi \)[/tex] radians is equivalent to [tex]\( 180^{\circ} \)[/tex].
The relationship between radians and degrees is:
[tex]\[
1 \text{ radian} = \frac{180^{\circ}}{\pi}
\][/tex]
Given the angle [tex]\(\frac{\pi}{4}\)[/tex] radians, to convert this angle to degrees, we will multiply it by the conversion factor:
[tex]\[
\frac{\pi}{4} \cdot \frac{180^{\circ}}{\pi}
\][/tex]
Now, let’s simplify the expression:
[tex]\[
\frac{\pi}{4} \cdot \frac{180^{\circ}}{\pi} = \left( \frac{\pi \cdot 180^{\circ}}{4 \cdot \pi} \right) = \left( \frac{180^{\circ}}{4} \right) = 45^{\circ}
\][/tex]
So, the conversion of [tex]\(\frac{\pi}{4}\)[/tex] radians to degrees results in:
[tex]\[
45^{\circ}
\][/tex]
Therefore, the expression that correctly converts [tex]\(\frac{\pi}{4}\)[/tex] radians to degrees is:
[tex]\[
\boxed{\frac{\pi}{4} \cdot \frac{180^\circ}{\pi}}
\][/tex]
