Answer:
[tex]x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}[/tex]
Step-by-step explanation:
Alright so being presented with this equation the first thing we want to do is subtract 1 from both sides of [tex]2\cos \left(x\right)+1=0[/tex].
[tex]2\cos \left(x\right)+1-1=0-1[/tex].
Now we want to simplify it to [tex]2\cos \left(x\right)=-1[/tex].
Now go ahead and divide both sides by 2. [tex]\frac{2\cos \left(x\right)}{2}=\frac{-1}{2}[/tex]
Make sure you simplify again to get [tex]\cos \left(x\right)=-\frac{1}{2}[/tex].
Now you need your sin/cos periodicity table. When you look at the charts. Look for the general solutions of [tex]\cos \left(x\right)=-\frac{1}{2}[/tex]. After looking at the chart you will find [tex]x=\frac{2\pi }{3}+2\pi n,\:x=\frac{4\pi }{3}+2\pi n[/tex].
Which we can then finalize at [tex]x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}[/tex].
Hope this helps!
