How many degrees is 3π/7 radians?
Understand the Problem
The question is asking to determine how many degrees correspond to a given angle in radians (3π/7 radians). This involves converting the angle from radians to degrees using the conversion factor 180/π.
Answer
The angle $\frac{3\pi}{7}$ radians is approximately $77.14$ degrees.
Answer for screen readers
The angle $\frac{3\pi}{7}$ radians corresponds to approximately $77.14$ degrees.
Steps to Solve
- Identify the conversion factor
To convert radians to degrees, we use the conversion factor:
$$ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} $$
- Substitute the value of radians into the formula
Given that the angle in radians is $\frac{3\pi}{7}$, substitute this into the conversion formula:
$$ \text{Degrees} = \frac{3\pi}{7} \times \frac{180}{\pi} $$
- Simplify the expression
Cancel $\pi$ in the numerator and the denominator:
$$ \text{Degrees} = \frac{3 \times 180}{7} $$
Now calculate the multiplication:
$$ \text{Degrees} = \frac{540}{7} $$
- Perform the division
Now divide $540$ by $7$ to find the final result:
$$ \text{Degrees} \approx 77.14 $$
The angle $\frac{3\pi}{7}$ radians corresponds to approximately $77.14$ degrees.
More Information
This calculation is useful in various fields such as physics and engineering, where converting between radians and degrees is often necessary for calculations involving angles.
Tips
- Forgetting the conversion factor: Always remember to multiply by $\frac{180}{\pi}$ to convert radians to degrees.
- Not simplifying the equation: It’s easy to skip canceling out $\pi$ before performing calculations, which can lead to misplaced calculations.
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