Convert 315 degrees to radians.
Understand the Problem
The question is asking to convert an angle measured in degrees (315 degrees) into its equivalent in radians. To do this, we will use the conversion factor that 1 degree is equal to rac{ ext{π}}{180} radians.
Answer
The angle 315 degrees is equivalent to $\frac{7\pi}{4}$ radians.
Answer for screen readers
The equivalent angle in radians is $\frac{7\pi}{4}$.
Steps to Solve
- Identify the conversion factor
We know that the conversion from degrees to radians is given by the formula:
$$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$
- Substitute the degree value
In this case, we are converting 315 degrees, so we substitute it into the formula:
$$ \text{radians} = 315 \times \frac{\pi}{180} $$
- Simplify the multiplication
Now let's simplify the fraction:
$$ \frac{315}{180} = \frac{315 \div 45}{180 \div 45} = \frac{7}{4} $$
- Combine with π
Now, we multiply by π:
$$ \text{radians} = \frac{7\pi}{4} $$
The equivalent angle in radians is $\frac{7\pi}{4}$.
More Information
The conversion from degrees to radians is commonly used in trigonometry, especially since many mathematical functions (like sine and cosine) are typically calculated using radians.
Tips
- A common mistake is forgetting to use the conversion factor properly.
- Another mistake is neglecting to simplify the fraction, which can lead to a more complicated answer that is harder to interpret.
