Question

1. \\(\frac{2pi}{3}\\)

Explanation:

Step1: Identify the problem type

The given expression is \(\frac{2\pi}{3}\), which is an angle in radians. If we assume the problem is to convert it to degrees (a common task with such angle measures), we use the conversion formula: \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \).

Step2: Apply the conversion formula

Substitute \(\text{Radians} = \frac{2\pi}{3}\) into the formula:

$$ \text{Degrees} = \frac{2\pi}{3} \times \frac{180^\circ}{\pi} $$

The \(\pi\) terms cancel out:

$$ \text{Degrees} = \frac{2}{3} \times 180^\circ $$

Calculate \(\frac{2}{3} \times 180^\circ\): \( 2 \times 60^\circ = 120^\circ \).

Answer:

If converting \(\frac{2\pi}{3}\) radians to degrees, the result is \(120^\circ\). If the problem was different (e.g., simplifying, finding coterminal angles, etc.), more context would be needed, but for the common conversion, \(120^\circ\) is the result.