To convert an angle measured in radians to degrees, you can use the conversion factor that [tex]\(180^\circ\)[/tex] is equivalent to [tex]\(\pi\)[/tex] radians. Here's a step-by-step process to convert [tex]\(\frac{5\pi}{3}\)[/tex] radians into degrees:
1. Write down the given radians:
[tex]\[
\frac{5\pi}{3} \text{ radians}
\][/tex]
2. Use the conversion factor:
[tex]\[
1 \text{ radian} = \frac{180^\circ}{\pi}
\][/tex]
3. Multiply the given radian measure by the conversion factor:
[tex]\[
\frac{5\pi}{3} \times \frac{180^\circ}{\pi}
\][/tex]
4. Cancel out the [tex]\(\pi\)[/tex] in the numerator and denominator:
[tex]\[
\frac{5 \times 180^\circ}{3}
\][/tex]
5. Simplify the multiplication and division:
[tex]\[
\frac{900^\circ}{3} = 300^\circ
\][/tex]
Therefore, [tex]\(\frac{5\pi}{3}\)[/tex] radians is equal to [tex]\(300^\circ\)[/tex].
