Express, in degrees, the angles with the following radian measures: 2(pi)/3

To convert a radian measure to degrees, we use the formula:

\[
\theta_{\text{degrees}} = \theta_{\text{radians}} \times \left( \frac{180^\circ}{\pi} \right)
\]

Given \( \theta_{\text{radians}} = \frac{2\pi}{3} \), we apply the formula:

\[
\theta_{\text{degrees}} = \frac{2\pi}{3} \times \frac{180^\circ}{\pi} 
\]

The \( \pi \)'s cancel out:

\[
\theta_{\text{degrees}} = \frac{2 \times 180^\circ}{3} = \frac{360^\circ}{3} = 120^\circ
\]

So, \( \frac{2\pi}{3} \) radians is equivalent to \( 120^\circ \).

Would you like any further details or clarifications? Here are some related questions for practice:

1. Convert \( \frac{5\pi}{6} \) radians to degrees.
2. What is \( \frac{\pi}{4} \) radians in degrees?
3. Express \( \frac{3\pi}{2} \) radians in degrees.
4. Convert 60 degrees to radians.
5. What is 45 degrees in radians?

**Tip**: To quickly convert between radians and degrees, remember that \( 180^\circ = \pi \) radians.

Discover how to convert 2(pi)/3 radians into degrees using the angle conversion formula. This example illustrates the cancellation of π and provides a step-by-step solution, resulting in 120 degrees. Ideal for students in Grades 7-10.

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