How is $3\pi-10$ element of $[-\pi/2,\pi/2]$?

Question

How is $3\pi-10$ element of $[-\pi/2,\pi/2]$? According to me this means that $530$ is an element of $[-90,90]$. i.e. Range of $\arcsin$ function.

(Note:- I was trying to find the value of $\arcsin(\sin 10))$)

Answer 1

You're making the mistake of not converting everything into degrees and just the $\pi$ into degrees.

$$(3\pi-10) rad = (540-10\times 57.296)^{\circ}$$

$$= -32.96^{\circ} \in [-90^{\circ},90^{\circ}]$$