How do you evaluate $arcsin(sin3)$ ?

Question

14501 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-21T08:25:13

$arcsin(sin(3))=pi-3$

Note that $arcsin$ maps $[-1,1]$ to $[-pi/2,pi/2]$ .

We need to find an angle $x in [-pi/2,pi/2]$ where $sin(x)=sin(3)$ .

Since $sin(x)$ is symmetric about $x=pi/2$ we have $sin(3)=sin(pi-3)$ . $pi-3$ is in $[-pi/2,pi/2]$ , therefore we have:

$arcsin(sin(3))=pi-3$

How do you evaluate arcsin(sin3)arcsin(sin3)?