Question

1. convert 120° to radians.

options:
\\(\frac{2pi}{3}\\)
\\(\frac{4pi}{3}\\)
\\(\frac{pi}{3}\\)
\\(\frac{5pi}{3}\\)

Explanation:

Step1: Recall degree to radian formula

To convert degrees to radians, use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180^\circ} \)

Step2: Substitute the given degree

Given \( 120^\circ \), substitute into the formula:
\( 120^\circ \times \frac{\pi}{180^\circ} \)

Step3: Simplify the fraction

Simplify \( \frac{120}{180} \) by dividing numerator and denominator by 60:
\( \frac{120 \div 60}{180 \div 60} = \frac{2}{3} \)
So, \( 120^\circ \times \frac{\pi}{180^\circ} = \frac{2\pi}{3} \)

Answer:

\( \frac{2\pi}{3} \) (corresponding to the first option: \( \boldsymbol{\frac{2\pi}{3}} \))