Question

solve the equations below exactly. Give your answers in radians, and find all possible values for t in the interval 0 < t < 2pi. enter your solutions in a comma separated list.

Answer 1

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.

`\begin{gathered} \sin t=-\frac{\sqrt[]{2}}{2} \\ t=\sin ^(-1)(-\frac{\sqrt[]{2}}{2})=225 \end{gathered}`

The first answer is t = 225°.

`\begin{gathered} \cos t=\frac{\sqrt[]{3}}{2} \\ t=\cos ^(-1)(\frac{\sqrt[]{3}}{2}) \\ t=30 \end{gathered}`

The second answer is 30°.

`\begin{gathered} \tan t=-\frac{1}{\sqrt[]{3}} \\ t=\tan ^(-1)(-\frac{1}{\sqrt[]{3}}) \\ t=150 \end{gathered}`

The third answer is t = 150°.