Unit Circle Math Example 2

Solution

1. 1
   $\theta=\frac{3\pi}{4}$ is in the second quadrant ($\frac{\pi}{2}<\frac{3\pi}{4}<\pi$). Reference angle: $\pi-\frac{3\pi}{4}=\frac{\pi}{4}$.
2. 2
   In Q2: $\cos<0$, $\sin>0$. From reference angle $\frac{\pi}{4}$: $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$, $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.
3. 3
   Apply signs: $\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}$, $\sin\frac{3\pi}{4}=+\frac{\sqrt{2}}{2}$. $\tan\frac{3\pi}{4}=\frac{\sin}{\cos}=\frac{\sqrt{2}/2}{-\sqrt{2}/2}=-1$.