Question

Show all work. URGENT

Answer 1

Answer:

2π/3&5π/3

Step-by-step explanation:

2 cos(x)+1=0

i.e, cos(x) =(-1/2)

i.e, cos(x)= - cos (π/3)

i.e, cos(x)= cos(π-π/3) [since, cos(π-x) = -cosX]

i.e, cos(x)=cos2π/3

x=2π/3

or, cos(x)= -cos(π/3)

i.e, cos(x)=cos(π+π/3). [since, cos (π+x)= -cosx]

x=4π/3

✌️:)

Answer 2

Answer:

$x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}$

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 $2\cos \left(x\right)+1=0$.

$2\cos \left(x\right)+1-1=0-1$.

Now we want to simplify it to $2\cos \left(x\right)=-1$.

Now go ahead and divide both sides by 2. $\frac{2\cos \left(x\right)}{2}=\frac{-1}{2}$

Make sure you simplify again to get $\cos \left(x\right)=-\frac{1}{2}$.

Now you need your sin/cos periodicity table. When you look at the charts. Look for the general solutions of $\cos \left(x\right)=-\frac{1}{2}$. After looking at the chart you will find $x=\frac{2\pi }{3}+2\pi n,\:x=\frac{4\pi }{3}+2\pi n$.

Which we can then finalize at $x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}$.

Hope this helps!