Question

Cum se calculeaza arcsin (-1)?​

Answer 1

$\it x = arcsin(-1) \Rightarrow sinx=sin(arcsin(-1)) \Rightarrow sinx=-1 \Rightarrow\\ \\ \Rightarrow x = - \dfrac{\pi}{2}$

$\it arcsinx\in\Big[-\dfrac{\pi}{2},\ \dfrac{\pi}{2}\Big],\ \ \forall x\in[-1,\ \ 1]$

Answer 2

$-\dfrac{\pi}{2}\leq \arcsin x\leq \dfrac{\pi}{2}\\\\\arcsin(-x) = -\arcsin x\\ \\\\ \Rightarrow \arcsin(-1) = -\arcsin 1 = -\dfrac{\pi}{2}$