Question

Use a graph to solve the equation on the interval

Answer 1

$sec(x)=-\sqrt{2}\qquad \begin{cases} sec(\theta)=\cfrac{1}{cos(\theta)} \end{cases} \\ \quad \\ \cfrac{1}{cos(x)}=-\sqrt{2}\implies \cfrac{1}{-\sqrt{2}}=cos(x) \\ \quad \\ cos^{-1}\left( \cfrac{1}{-\sqrt{2}} \right)=cos^{-1}[cos(x)] \\ \quad \\ cos^{-1}\left(- \cfrac{1}{\sqrt{2}} \right)=x \\ \quad \\ \textit{now, check your Unit Circle for those }\measuredangle x$