Finding the Values of Trigonometric Functions

Find the values of the six trigonometric functions of angle $t$ based on Figure 9.

Figure 9

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\begin{matrix} sin t & = y & = - \frac{\sqrt{3}}{2} \\ cos t & = x & = - \frac{1}{2} \\ tan t & = \frac{sin t}{cos t} & = \frac{- \frac{\sqrt{3}}{2}}{- \frac{1}{2}} & = \sqrt{3} \\ sec t & = \frac{1}{cos t} & = \frac{1}{- \frac{1}{2}} & = −2 \\ csc t & = \frac{1}{sin t} & = \frac{1}{- \frac{\sqrt{3}}{2}} & = - \frac{2 \sqrt{3}}{3} \\ cot t & = \frac{1}{tan t} & = \frac{1}{\sqrt{3}} & = \frac{\sqrt{3}}{3} \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the values of the six trigonometric functions of angle $t$ based on Figure 10.

Figure 10

How did it go?