Convert 2pi/9 from radians to degrees.
Understand the Problem
The question is asking to convert the angle given in radians (2pi/9) into degrees. To do this, we can multiply the radian measure by (180/pi) to get the equivalent angle in degrees.
Answer
$40$ degrees
Answer for screen readers
The angle $\frac{2\pi}{9}$ radians is equal to $40$ degrees.
Steps to Solve
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Identify the conversion factor To convert radians to degrees, we use the conversion factor $\frac{180}{\pi}$.
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Set up the equation Multiply the given radian value $\frac{2\pi}{9}$ by the conversion factor: $$ \text{Degrees} = \frac{2\pi}{9} \times \frac{180}{\pi} $$
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Simplify the expression When multiplying, the $\pi$ in the numerator and denominator will cancel each other out: $$ \text{Degrees} = \frac{2 \times 180}{9} $$
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Perform the multiplication Calculate the numerator: $$ 2 \times 180 = 360 $$
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Divide to get the final answer Now divide by 9: $$ \text{Degrees} = \frac{360}{9} = 40 $$
The angle $\frac{2\pi}{9}$ radians is equal to $40$ degrees.
More Information
Converting between radians and degrees is a common skill in trigonometry. Remember, there are $180$ degrees in $\pi$ radians, which is why we use the conversion factor $\frac{180}{\pi}$.
Tips
- Forgetting to simplify: Many people sometimes forget to simplify the expression after setting it up, leading to incorrect intermediate values. Always remember to simplify whenever possible.
- Confusing radians with degrees: Make sure to keep track of which unit you are working with, especially during conversions.
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