Finding the Value of Trigonometric Functions

If $\sin (t) = - \frac{\sqrt{3}}{2} and cos (t) = \frac{1}{2}, find sec (t), csc (t), tan (t), cot (t) .$

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

Your turn

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

$\sin (t) = \frac{\sqrt{2}}{2} and \cos (t) = \frac{\sqrt{2}}{2}, find sec (t), csc (t), tan (t), and cot (t)$

How did it go?