To convert an angle from degrees to radians, we use the conversion factor [tex]\(\frac{\pi}{180}\)[/tex]. Specifically, to convert [tex]\(36^\circ\)[/tex] to radians:
1. Start with the given angle in degrees: [tex]\(36^\circ\)[/tex].
2. Use the conversion factor [tex]\(\frac{\pi}{180}\)[/tex]:
[tex]\[
36^\circ \times \frac{\pi}{180}
\][/tex]
3. Simplify the expression:
[tex]\[
36 \times \frac{\pi}{180} = \frac{36\pi}{180}
\][/tex]
4. Simplify the fraction [tex]\(\frac{36}{180}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 36:
[tex]\[
\frac{36\pi}{180} = \frac{36 \div 36 \pi}{180 \div 36} = \frac{\pi}{5}
\][/tex]
Thus, [tex]\(36^\circ\)[/tex] in radians, as a multiple of [tex]\(\pi\)[/tex], is [tex]\(\frac{\pi}{5}\)[/tex].
Therefore, the correct answer is:
C
