To find each answer, we just have to solve for t. It is important to use the important angles in trigonometry to provide an exact answer.
[tex]\begin{gathered} \sin t=-\frac{\sqrt[]{2}}{2} \\ t=\sin ^{-1}(-\frac{\sqrt[]{2}}{2})=225 \end{gathered}[/tex]The first answer is t = 225°.
[tex]\begin{gathered} \cos t=\frac{\sqrt[]{3}}{2} \\ t=\cos ^{-1}(\frac{\sqrt[]{3}}{2}) \\ t=30 \end{gathered}[/tex]The second answer is 30°.
[tex]\begin{gathered} \tan t=-\frac{1}{\sqrt[]{3}} \\ t=\tan ^{-1}(-\frac{1}{\sqrt[]{3}}) \\ t=150 \end{gathered}[/tex]The third answer is t = 150°.