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.
Answer
120^{\circ}
Answer for screen readers
The final answer is 120 degrees
Steps to Solve
- Identify the conversion factor from radians to degrees
To convert radians to degrees, use the conversion factor $180^{\circ}$ for every $\pi$ radians.
- Set up the conversion equation
Multiply the given radians by the conversion factor: $$ \frac{2\pi}{3} \times \frac{180^{\circ}}{\pi} $$
- Simplify the equation
Cancel out $\pi$ in the equation: $$ \frac{2}{3} \times 180^{\circ} $$
- Perform the multiplication
Calculate: $$ \frac{2 \times 180^{\circ}}{3} = 120^{\circ} $$
The final answer is 120 degrees
More Information
Degrees and radians are two units for measuring angles. An angle of 360 degrees is equal to $2\pi$ radians.
Tips
A common mistake is forgetting to cancel $\pi$ in the conversion step. Make sure to always simplify the equation before performing the multiplication.
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