Answer :
To convert an angle from degrees to radians, we can use the formula:
[tex]\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
Given the angle [tex]\(\theta = 240^\circ\)[/tex], we can find its measurement in radians by performing the following calculation:
1. Substitute [tex]\(\theta = 240^\circ\)[/tex] into the formula:
[tex]\[ \theta_\text{radians} = 240^\circ \times \left(\frac{\pi}{180}\right) \][/tex]
2. Simplify the fraction:
[tex]\[ \theta_\text{radians} = 240 \times \left(\frac{\pi}{180}\right) = \frac{240\pi}{180} \][/tex]
3. Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 60:
[tex]\[ \frac{240\pi}{180} = \frac{240 \div 60 \pi}{180 \div 60} = \frac{4\pi}{3} \][/tex]
Hence, the measurement of [tex]\(\theta\)[/tex] in radians is:
[tex]\[ \theta_\text{radians} = \frac{4}{3} \pi \][/tex]
So, the correct answer is:
C. [tex]\(\theta = \frac{4}{3} \pi\)[/tex] radians
[tex]\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
Given the angle [tex]\(\theta = 240^\circ\)[/tex], we can find its measurement in radians by performing the following calculation:
1. Substitute [tex]\(\theta = 240^\circ\)[/tex] into the formula:
[tex]\[ \theta_\text{radians} = 240^\circ \times \left(\frac{\pi}{180}\right) \][/tex]
2. Simplify the fraction:
[tex]\[ \theta_\text{radians} = 240 \times \left(\frac{\pi}{180}\right) = \frac{240\pi}{180} \][/tex]
3. Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 60:
[tex]\[ \frac{240\pi}{180} = \frac{240 \div 60 \pi}{180 \div 60} = \frac{4\pi}{3} \][/tex]
Hence, the measurement of [tex]\(\theta\)[/tex] in radians is:
[tex]\[ \theta_\text{radians} = \frac{4}{3} \pi \][/tex]
So, the correct answer is:
C. [tex]\(\theta = \frac{4}{3} \pi\)[/tex] radians
