To convert [tex]\(50^{\circ}\)[/tex] to radian measure in terms of [tex]\(\pi\)[/tex]:
1. Understand the conversion factor:
To convert degrees to radians, we use the conversion factor [tex]\(\frac{\pi}{180}\)[/tex], because [tex]\(180^{\circ} \equiv \pi\)[/tex] radians.
2. Apply the conversion:
Multiply the degree measure by the conversion factor.
[tex]\[
50^{\circ} \times \frac{\pi}{180}
\][/tex]
3. Perform the multiplication:
[tex]\[
50 \times \frac{\pi}{180} = \frac{50\pi}{180}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{50\pi}{180} = \frac{5\pi}{18}
\][/tex]
Thus, the radian measure of [tex]\(50^{\circ}\)[/tex] in terms of [tex]\(\pi\)[/tex] is [tex]\(\frac{5\pi}{18}\)[/tex].
Now, let's compare this with the given options:
- [tex]\(\frac{5}{27} \pi\)[/tex]
- [tex]\(\frac{5}{9} \pi\)[/tex]
- [tex]\(\frac{5}{18} \pi\)[/tex]
- [tex]\(\frac{5}{36} \pi\)[/tex]
Clearly, [tex]\(\frac{50^\circ}\)[/tex] in radian measure corresponds to the option [tex]\(\frac{5}{18} \pi\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{\frac{5}{18} \pi}
\][/tex]
