Finding the Exact Value Using the Formula for the Sum of Two Angles for Cosine

Find the exact value of $\cos (75°) .$

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
As $75° = 45° + 30°,$ we can evaluate $\cos (75°)$ as $\cos (45° + 30°) .$
$\begin{matrix} \cos (α + β) & = & \cos α \cos β - \sin α \sin β \\ \cos (45° + 30°) & = & \cos (45°) \cos (30°) - \sin (45°) \sin (30°) \\ = & \frac{\sqrt{2}}{2} (\frac{\sqrt{3}}{2}) - \frac{\sqrt{2}}{2} (\frac{1}{2}) \\ = & \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} \\ = & \frac{\sqrt{6} - \sqrt{2}}{4} \end{matrix}$
Keep in mind that we can always check the answer using a graphing calculator in degree mode.

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 $\cos (105°) .$

How did it go?