Answer:
[tex]$x=\frac{\pi }{3}+2\pi n, n\in \mathbb{Z}$[/tex]
[tex]$\:x=\frac{5\pi }{3}+2\pi n, n \in \mathbb{Z}$[/tex]
[tex]$x=\frac{2\pi }{3}+2\pi n, n\in \mathbb{Z}$[/tex]
[tex]$\:x=\frac{4\pi }{3}+2\pi n, n \in \mathbb{Z}$[/tex]
or
[tex]$x=\frac{\pi}{3}+\pi n, n \in \mathbb{Z} $[/tex]
[tex]$x=\frac{2\pi }{3}+\pi n, n\in \mathbb{Z}$[/tex]
Step-by-step explanation:
[tex]4\text{cos}^2(x)-1=0\\4\text{cos}^2(x)=1\\[/tex]
[tex]$cos(x)=\pm\sqrt{\frac{1}{4} } $[/tex]
[tex]$cos(x)=\pm\frac{1}{2} $[/tex]
So, when cos(x) is equal to
[tex]$\frac{1}{2} \text{ and } -\frac{1}{2}$[/tex] ?
For
[tex]$cos(x)=\frac{1}{2} $[/tex]
We are talking about x = 60º and x = 300º, Quadrant I and IV, respectively. In radians:
[tex]$x=\frac{\pi }{3}+2\pi n, n\in \mathbb{Z}$[/tex]
[tex]$\:x=\frac{5\pi }{3}+2\pi n, n \in \mathbb{Z}$[/tex]
or
[tex]$x=\frac{\pi}{3}+\pi n, n \in \mathbb{Z} $[/tex]
For
[tex]$cos(x)=-\frac{1}{2} $[/tex]
We are talking about x = 120º and x = 240º, Quadrant II and III, respectively. In radians:
[tex]$x=\frac{2\pi }{3}+2\pi n, n\in \mathbb{Z}$[/tex]
[tex]$\:x=\frac{4\pi }{3}+2\pi n, n \in \mathbb{Z}$[/tex]
or
[tex]$x=\frac{2\pi }{3}+\pi n, n\in \mathbb{Z}$[/tex]
