# How do you convert 5 radians to degree?

Nov 7, 2015

$\approx 286$

#### Explanation:

To convert radians to degrees, simply multiply it by $\frac{180}{\pi}$ to get your answer.

Why? Because $1 \pi$ is $180$ degrees, and $2 \pi$ is $360$ degrees. To convert one unit to another, I would want to cancel out the units. Just like how i want to convert 1 minute to seconds, I would do $\cancel{1 m} \cdot \frac{60}{\cancel{1 m}}$ leaving me with $60$ seconds.

Example:
If you have $\pi$ and you wanted to convert that to degrees, you would want to cancel out the $\pi$ by multiplying it by $\frac{180}{\pi}$.

so $\cancel{\pi} \cdot \frac{180}{\cancel{\pi}}$ is 180.

On the other hand, if you want to convert degrees to radians, multiply your degrees by $\frac{\pi}{180}$ so the degrees cancel out.

Example:
If I wanted to convert 150 degrees to radians:

$150 \cdot \frac{\pi}{180} = \frac{5 \pi}{6} \approx 2.61$