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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

  1. Write the conversion factor for degrees to radians

The conversion from degrees to radians is given by the formula:

$$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$

  1. Substitute 720 degrees into the formula

Next, substitute $720$ for degrees into the formula.

$$ \text{radians} = 720 \times \frac{\pi}{180} $$

  1. Simplify the expression

Now, simplify the multiplication:

$$ \text{radians} = \frac{720\pi}{180} $$

  1. Simplify the fraction further

Divide the numerator and the denominator by their greatest common divisor (GCD), which is 180:

$$ \text{radians} = \frac{720 \div 180}{180 \div 180}\pi = \frac{4}{1}\pi = 4\pi $$

  1. 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.
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