To convert an angle from degrees to radians, we use the conversion factor:
[tex]\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \][/tex]
Given an angle of [tex]\( 270^\circ \)[/tex]:
1. Multiply the angle in degrees by the conversion factor:
[tex]\[
270^\circ \times \frac{\pi}{180}
\][/tex]
2. Simplify the expression:
- The degrees cancel out, leaving us with the fraction:
[tex]\[
\frac{270 \pi}{180}
\][/tex]
- Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 90:
[tex]\[
\frac{270 \div 90}{180 \div 90} \pi = \frac{3 \pi}{2}
\][/tex]
Therefore, [tex]\( 270^\circ \)[/tex] converted to radians is:
[tex]\[ \frac{3 \pi}{2} \][/tex]
Comparing this result with the answer choices provided:
[tex]\[
\frac{\pi}{6}, \quad \frac{3}{2}, \quad \frac{3 \pi}{2}, \quad 3
\][/tex]
The correct answer is:
[tex]\[ \boxed{\frac{3\pi}{2}} \][/tex]
