2pi/3 in degrees

Understand the Problem

The question is asking us to convert the angle 2pi/3 radians to degrees. To solve this, we will use the conversion factor that 180 degrees is equal to pi radians.

120^{\circ}

The final answer is 120 degrees

Steps to Solve

1. Identify the conversion factor from radians to degrees

To convert radians to degrees, use the conversion factor $180^{\circ}$ for every $\pi$ radians.

1. Set up the conversion equation

Multiply the given radians by the conversion factor: $$\frac{2\pi}{3} \times \frac{180^{\circ}}{\pi}$$

1. Simplify the equation

Cancel out $\pi$ in the equation: $$\frac{2}{3} \times 180^{\circ}$$

1. Perform the multiplication

Calculate: $$\frac{2 \times 180^{\circ}}{3} = 120^{\circ}$$

The final answer is 120 degrees

Degrees and radians are two units for measuring angles. An angle of 360 degrees is equal to $2\pi$ radians.
A common mistake is forgetting to cancel $\pi$ in the conversion step. Make sure to always simplify the equation before performing the multiplication.