Question

Find the angle(s) that satisfy the given values in the interval [0, 2π)

Answer 1

1.

`\begin{gathered} \cos (x)=-(1)/(2) \\ x\in\lbrack0,2\pi) \end{gathered}`

Take the inverse cosine of both sides:

`\begin{gathered} x=(2\pi)/(3) \\ or \\ x=(4\pi)/(3) \end{gathered}`

2.

`\begin{gathered} \sec (x)=\sqrt[]{2} \\ (1)/(\cos (x))=\sqrt[]{2} \\ \cos (x)=\frac{1}{\sqrt[]{2}} \end{gathered}`

Take the inverse cosine of both sides:

`\begin{gathered} x=(\pi)/(4) \\ or \\ x=(7\pi)/(4) \end{gathered}`

3.

`\begin{gathered} \cot (x)=-\frac{\sqrt[]{3}}{3} \\ (1)/(\tan (x))=-\frac{\sqrt[]{3}}{3} \\ \tan (x)=-\frac{3}{\sqrt[]{3}} \end{gathered}`

Take the inverse tangent of both sides:

`\begin{gathered} x=(2\pi)/(3) \\ or \\ x=(5\pi)/(3) \end{gathered}`

4.

`\sin (x)=-1`

Take the inverse sine of both sides:

`x=(3\pi)/(2)`