Question

sin^-1(sin9pi/7)
can someone help me by explaining how I can find the angle that lies in the interval [-2/pi,2/pi] to get the correct answer?

Answer 1

Note that \(x \) is a solution for \(\sin^{-1}(\sin (x))\), but it's not the only solution for obvious reasons.

Answer 2

\(x + 2\pi\), \(x - 2\pi\) are solutions too.

Answer 3

So \(9\pi/7\) is a solution.

Answer 4

thank you for the explanation. what if it was [-pi/2,pi/2] ? what would that change?

Answer 5

Remember the graph of sine. That always helps ya.