Sine and Cosine Function Values

In 3.2B we learned that the terminal ray of $\theta$ meets the unit circle at the point $(\cos \theta , \sin \theta )$. For most angles, those coordinates are messy decimals that need a calculator. But for a handful of special angles — multiples of $\pi /6$ and $\pi /4$ — we can find the exact values using nothing more than the Pythagorean theorem and symmetry. These angles appear again and again in the rest of the course, so this note builds them from scratch rather than asking you to memorize a chart.