To find the radian equivalent of [tex]\(180^\circ\)[/tex], we'll use the fact that [tex]\(180^\circ\)[/tex] is a special angle in the unit circle.
1. Understanding Degrees and Radians:
- One complete revolution (a circle) is [tex]\(360^\circ\)[/tex].
- The same complete revolution in radians is [tex]\(2\pi\)[/tex] radians.
2. Relating Degrees to Radians:
- We can set up a proportion to relate degrees and radians. Specifically, we know that [tex]\(360^\circ\)[/tex] corresponds to [tex]\(2\pi\)[/tex] radians.
3. Setting up the Proportion:
- To find the radian measure for [tex]\(180^\circ\)[/tex], observe that [tex]\(180^\circ\)[/tex] is half of [tex]\(360^\circ\)[/tex].
- Therefore, the radian measure should be half of [tex]\(2\pi\)[/tex] radians.
4. Calculating the Radian Equivalent:
- [tex]\[
\text{Radian equivalent of } 180^\circ = \frac{1}{2} \times 2\pi = \pi \text{ radians}
\][/tex]
So, the radian equivalent of [tex]\(180^\circ\)[/tex] is [tex]\(\pi\)[/tex] radians.
Thus, the correct answer is:
[tex]\[
\pi \text{ radians}
\][/tex]
