Sure! Let's convert [tex]\( 720^\circ \)[/tex] to radians with a step-by-step solution.
1. Understand the Conversion Factor:
- To convert degrees to radians, we use the conversion factor [tex]\(\frac{\pi \text{ radians}}{180^\circ}\)[/tex]. This means that [tex]\(1^\circ = \frac{\pi}{180} \text{ radians}\)[/tex].
2. Write the Conversion Formula:
[tex]\[
\text{Radians} = \text{Degrees} \times \frac{\pi \text{ radians}}{180^\circ}
\][/tex]
3. Apply this Formula to [tex]\(720^\circ\)[/tex]:
[tex]\[
720^\circ \times \frac{\pi \text{ radians}}{180^\circ}
\][/tex]
4. Simplify the Multiplication:
- Multiply [tex]\(720\)[/tex] by [tex]\(\frac{\pi}{180}\)[/tex]:
[tex]\[
720 \times \frac{\pi}{180} = \frac{720\pi}{180}
\][/tex]
5. Perform the Division:
- Divide [tex]\(720\)[/tex] by [tex]\(180\)[/tex]:
[tex]\[
\frac{720}{180} = 4
\][/tex]
Therefore:
[tex]\[
\frac{720\pi}{180} = 4\pi
\][/tex]
6. Final Conversion:
- Hence, [tex]\(720^\circ\)[/tex] converted to radians is [tex]\(4\pi\)[/tex].
So, the correct answer is:
[tex]\[ 4\pi \][/tex]
