Răspuns:
Explicație pas cu pas:
a.
[tex]arcsin(sin(2x+\frac{\pi }{6} )=arcsin(-\frac{1}{2})\\ 2x+\frac{\pi }{6}=-\frac{\pi }{6} \\ 2x=-\frac{\pi }{3}\\ x=-\frac{\pi }{6}\\ x=\pi n+\frac{\pi }{2};x=\pi n+\frac{5\pi }{6}[/tex]
b.
[tex]-cos(x+\frac{\pi }{4})=1\\ cos(x+\frac{\pi }{4})=-1\\ arccos(cos(x+\frac{\pi }{4} )=arccos(-1)\\ x+\frac{\pi }{4}=\pi\\ x=\frac{3\pi }{4}\\ x=2\pi n+\frac{3\pi }{4}[/tex]
c.
[tex]cos(\frac{x}{3})=-\frac{1}{2} \\ arccos(cos(\frac{x}{3} ))=arccos(-\frac{1}{2} )\\ \frac{x}{3} =\frac{2\pi }{3}\\ x=2\pi \\ x=2\pi +6\pi n;x=4\pi +6\pi n[/tex]
