To convert an angle from degrees to radians, we use the conversion formula:
[tex]\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \][/tex]
Let's apply this formula to convert [tex]\( 120^{\circ} \)[/tex] to radians:
[tex]\[ 120^{\circ} \times \frac{\pi}{180} \][/tex]
Now, we perform the multiplication:
[tex]\[ \frac{120 \pi}{180} \][/tex]
Next, we simplify the fraction:
[tex]\[ \frac{120}{180} = \frac{2}{3} \][/tex]
Thus, the angle in radians is:
[tex]\[ \frac{2 \pi}{3} \][/tex]
Now, we compare this result to the given options:
A. [tex]\( \frac{2 \pi}{3} \)[/tex] radians ⟵ This matches our result.
B. [tex]\( \frac{3 \pi}{2} \)[/tex] radians
C. [tex]\( \frac{3 \pi}{4} \)[/tex] radians
D. [tex]\( \frac{5 \pi}{6} \)[/tex] radians
The correct answer is:
A. [tex]\( \frac{2 \pi}{3} \)[/tex] radians
So, the angle [tex]\( 120^{\circ} \)[/tex] converted to radians is [tex]\( \frac{2 \pi}{3} \)[/tex].
