Convert 720 degrees to radians.
Understand the Problem
The question is asking us to convert 720 degrees into radians, which involves using the conversion factor that , 180 \degree = \pi \text{ radians}. To solve this, we will multiply 720 by \frac{\pi}{180}.
Answer
$4\pi$
Answer for screen readers
The conversion of 720 degrees into radians is $4\pi$.
Steps to Solve
- Write the conversion factor for degrees to radians
The conversion from degrees to radians is given by the formula:
$$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$
- Substitute 720 degrees into the formula
Next, substitute $720$ for degrees into the formula.
$$ \text{radians} = 720 \times \frac{\pi}{180} $$
- Simplify the expression
Now, simplify the multiplication:
$$ \text{radians} = \frac{720\pi}{180} $$
- Simplify the fraction further
Divide the numerator and the denominator by their greatest common divisor (GCD), which is 180:
$$ \text{radians} = \frac{720 \div 180}{180 \div 180}\pi = \frac{4}{1}\pi = 4\pi $$
- Final answer
Thus, we find that:
$$ \text{radians} = 4\pi $$
The conversion of 720 degrees into radians is $4\pi$.
More Information
The conversion from degrees to radians is important in trigonometry and calculus. Radians are often preferred in mathematical analysis as they provide a direct relationship between angular measures and linear distances on a circle.
Tips
- Forgetting to reduce the fraction when simplifying can lead to incorrect answers. Always check if the numerator and denominator can be divided by a common factor.
