720 degrees in radians
Understand the Problem
The question is asking how to convert 720 degrees into radians. To solve this, we will use the conversion factor that π radians is equal to 180 degrees.
Answer
$4\pi$
Answer for screen readers
The final answer is $4\pi$ radians.
Steps to Solve
- Identify the conversion factor
To convert degrees to radians, we know that $180$ degrees is equivalent to $\pi$ radians. We can set up the conversion factor as follows:
$$ \text{Conversion Factor} = \frac{\pi , \text{radians}}{180 , \text{degrees}} $$
- Set up the conversion
We need to convert $720$ degrees into radians by multiplying it by the conversion factor we found:
$$ \text{Radians} = 720 , \text{degrees} \times \frac{\pi , \text{radians}}{180 , \text{degrees}} $$
- Perform the multiplication
Now, we will simplify the multiplication:
$$ \text{Radians} = 720 \times \frac{\pi}{180} $$
- Simplify the expression
To simplify, we can reduce $720$ and $180$:
$$ \text{Radians} = \frac{720}{180} \cdot \pi $$
Calculating $\frac{720}{180}$ gives us $4$:
$$ \text{Radians} = 4\pi $$
The final answer is $4\pi$ radians.
More Information
The conversion from degrees to radians is often used in trigonometry and calculus. Knowing how to switch between these two units allows for easier understanding of angles in various mathematical contexts.
Tips
A common mistake is forgetting to simplify the fraction after using the conversion factor, which can lead to an incorrect answer. Always make sure to reduce the numbers when applicable.
