Convert 13pi/6 radians to degrees.
Understand the Problem
The question is asking to convert the angle given in radians (13π/6) into degrees. To do this, we will use the formula for converting radians to degrees, which is Degrees = Radians × (180/π).
Answer
$ 390 $ degrees
Answer for screen readers
The angle $ \frac{13\pi}{6} $ radians is equal to $ 390 $ degrees.
Steps to Solve
- Identify the formula for conversion
We will use the formula to convert radians to degrees:
$$ \text{Degrees} = \text{Radians} \times \left( \frac{180}{\pi} \right) $$
- Substitute the given value
Now we will substitute the given value of the angle in radians, which is $ \frac{13\pi}{6} $, into the formula:
$$ \text{Degrees} = \frac{13\pi}{6} \times \left( \frac{180}{\pi} \right) $$
- Simplify the expression
Cancel the $ \pi $ in the numerator and denominator:
$$ \text{Degrees} = \frac{13 \times 180}{6} $$
- Calculate the multiplication and division
Next, we calculate the multiplication and then divide by 6:
First calculate $ 13 \times 180 = 2340 $.
Then divide by 6:
$$ \text{Degrees} = \frac{2340}{6} = 390 $$
- State the final result
Thus, the angle $ \frac{13\pi}{6} $ radians is equal to $ 390 $ degrees.
The angle $ \frac{13\pi}{6} $ radians is equal to $ 390 $ degrees.
More Information
When converting angles from radians to degrees, remember that there are 360 degrees in a full circle. Thus, $ 390 $ degrees exceeds a full rotation and can also be expressed in a normalized form as $ 30 $ degrees (since $ 390 - 360 = 30 $).
Tips
- Forgetting to simplify the fraction after multiplying may lead to incorrect answers. Always simplify your results.
- Not cancelling $ \pi $ when you have it in both the numerator and denominator can lead to mistakes in calculation.
