Convert 9pi/4 to degrees.
Understand the Problem
The question is asking for the conversion of the angle measured in radians (9Ï€/4) to degrees. To solve this, we will use the conversion factor that Ï€ radians equals 180 degrees.
Answer
$405$ degrees
Answer for screen readers
The angle of $9\frac{\pi}{4}$ radians is equal to $405$ degrees.
Steps to Solve
- Identify the conversion factor
We know that $\pi$ radians is equal to 180 degrees. We will use this relationship to convert radians to degrees.
- Set up the conversion
To convert $9\pi/4$ radians to degrees, we multiply by the conversion factor $\frac{180 \text{ degrees}}{\pi \text{ radians}}$:
$$ \text{Degrees} = \frac{9\pi}{4} \times \frac{180}{\pi} $$
- Simplify the expression
Notice that the $\pi$ in the numerator and denominator will cancel each other out:
$$ \text{Degrees} = \frac{9 \times 180}{4} $$
- Calculate the value
Now we will do the multiplication and division:
$$ \text{Degrees} = \frac{1620}{4} = 405 \text{ degrees} $$
The angle of $9\frac{\pi}{4}$ radians is equal to $405$ degrees.
More Information
When converting angles from radians to degrees, remember that one complete revolution corresponds to $360$ degrees. An angle of $405$ degrees means that it is more than one full circle (360 degrees) and can also be expressed as $45$ degrees (i.e., $405 - 360 = 45$).
Tips
- Forgetting to cancel out $\pi$ while simplifying the expression can lead to incorrect results. Always remember to check if there's a common factor to reduce.