Răspuns:
3π - 10
Explicație pas cu pas:
[tex]\arcsin(\sin x) = \begin{cases} x,\ x\in\Big[-\dfrac{\pi}{2},\dfrac{\pi}{2}\Big]\\ \\ \pi - x,\ x\in \Big[\dfrac{\pi}{2},\dfrac{3\pi}{2}\Big]\\ \\ x-2\pi,\, x\in \Big[\dfrac{3\pi}{2},\dfrac{5\pi}{2}\Big] \\ \\3\pi-x,\x\in \Big[\dfrac{5\pi}{2},\dfrac{7\pi}{2}\Big]\\ \\ \text{si tot asa...}\end{cases}[/tex]
[tex]a = \arcsin(\sin 10) \\ \\ 10=x \cdot 3.14 \Rightarrow x = \dfrac{10}{3.14} \approx 3.18\\ \\ \Rightarrow 10 \approx 3.18 \pi \Rightarrow 10\in \Big[\dfrac{5\pi}{2},\dfrac{7\pi}{2}\Big] \\ \\ \Rightarrow \boxed{a = 3\pi - 10 }[/tex]
