Answer:
4π/9, 0.44444π, or 1.3962634 radians
Step-by-step explanation:
To convert from degrees, to radians, multiply the the degrees times pi over 180 degrees
![\textdegree *\frac{\pi }{180\textdegree}](https://tex.z-dn.net/?f=%5Ctextdegree%20%2A%5Cfrac%7B%5Cpi%20%20%7D%7B180%5Ctextdegree%7D)
We want to convert 80 degrees to radians.
![80 \textdegree *\frac{\pi}{180 \textdegree}](https://tex.z-dn.net/?f=80%20%5Ctextdegree%20%2A%5Cfrac%7B%5Cpi%7D%7B180%20%5Ctextdegree%7D)
The degrees signs cancel.
![80 *\frac{\pi}{180}](https://tex.z-dn.net/?f=80%20%2A%5Cfrac%7B%5Cpi%7D%7B180%7D)
![\frac {80}{1} *\frac{\pi}{180}](https://tex.z-dn.net/?f=%5Cfrac%20%7B80%7D%7B1%7D%20%2A%5Cfrac%7B%5Cpi%7D%7B180%7D)
Move 80 to the numerator.
![\frac{80 \pi}{180}](https://tex.z-dn.net/?f=%5Cfrac%7B80%20%5Cpi%7D%7B180%7D)
Simplify 80/180. Both the numerator and denominator can be divided by 20.
![\frac{(80/20) \pi}{180/20}](https://tex.z-dn.net/?f=%5Cfrac%7B%2880%2F20%29%20%5Cpi%7D%7B180%2F20%7D)
![\frac{4 \pi}{9} \approx 0.444444\pi \approx 1.3962634](https://tex.z-dn.net/?f=%5Cfrac%7B4%20%20%5Cpi%7D%7B9%7D%20%5Capprox%200.444444%5Cpi%20%5Capprox%201.3962634)
80 degrees is equal to 4π/9 radians, 0.44444π radians, or 1.3962634 radians.