Find the Exact Value of arcsin(sin(5pi/9))

[math_help]

1. Find the exact value of the expression arcsin(sin(5pi/9))



2. 5pi/9 = 100 degrees and pi/9 = 20 degrees



3. Tried pi/9 but it is wrong

 

[luju]

SO, 5pi/9 is 100 degree. So take sin of that. And do the arc sin of that.
Sin(5pi/9) = .9848

arcsin(.9848) = 80 degrees

 

[HallsofIvy]

1. Find the exact value of the expression arcsin(sin(5pi/9))



2. 5pi/9 = 100 degrees and pi/9 = 20 degrees



3. Tried pi/9 but it is wrong

Because sine is periodic, it doesn't have a true "inverse". The usual definition of Arcsine gives a value between $-pi/2$ and $\pi/2$. $5\pi/9$ is not in that range. Use the facts that $sin(x+ 2\pi)= sin(x)$ and $sin(\pi- x)= - sin(x)$.