Evaluating Trigonometric Functions of Special Angles Using Side Lengths

Find the exact value of the trigonometric functions of $\frac{π}{3},$ using side lengths.

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
$\begin{matrix} \sin (\frac{π}{3}) & = \frac{opp}{hyp} & = \frac{\sqrt{3 s}}{2 s} & = \frac{\sqrt{3}}{2} \\ \cos (\frac{π}{3}) & = \frac{adj}{hyp} & = \frac{s}{2 s} & = \frac{1}{2} \\ \tan (\frac{π}{3}) & = \frac{opp}{adj} & = \frac{\sqrt{3} s}{s} & = \sqrt{3} \\ \sec (\frac{π}{3}) & = \frac{hyp}{adj} & = \frac{2 s}{s} & = 2 \\ \csc (\frac{π}{3}) & = \frac{hyp}{opp} & = \frac{2 s}{\sqrt{3} s} & = \frac{2}{\sqrt{3}} & = \frac{2 \sqrt{3}}{3} \\ \cot (\frac{π}{3}) & = \frac{adj}{opp} & = \frac{s}{\sqrt{3} s} & = \frac{1}{\sqrt{3}} & = \frac{\sqrt{3}}{3} \end{matrix}$

Your turn

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

Find the exact value of the trigonometric functions of $\frac{π}{4},$ using side lengths.

How did it go?