1.
[tex]\begin{gathered} \cos (x)=-\frac{1}{2} \\ x\in\lbrack0,2\pi) \end{gathered}[/tex]
Take the inverse cosine of both sides:
[tex]\begin{gathered} x=\frac{2\pi}{3} \\ or \\ x=\frac{4\pi}{3} \end{gathered}[/tex]
2.
[tex]\begin{gathered} \sec (x)=\sqrt[]{2} \\ \frac{1}{\cos (x)}=\sqrt[]{2} \\ \cos (x)=\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]
Take the inverse cosine of both sides:
[tex]\begin{gathered} x=\frac{\pi}{4} \\ or \\ x=\frac{7\pi}{4} \end{gathered}[/tex]
3.
[tex]\begin{gathered} \cot (x)=-\frac{\sqrt[]{3}}{3} \\ \frac{1}{\tan (x)}=-\frac{\sqrt[]{3}}{3} \\ \tan (x)=-\frac{3}{\sqrt[]{3}} \end{gathered}[/tex]
Take the inverse tangent of both sides:
[tex]\begin{gathered} x=\frac{2\pi}{3} \\ or \\ x=\frac{5\pi}{3} \end{gathered}[/tex]
4.
[tex]\sin (x)=-1[/tex]
Take the inverse sine of both sides:
[tex]x=\frac{3\pi}{2}[/tex]
