Answer
1. $(1,0), sint=0, cost=1$
2. $( \frac{\sqrt 3}{2}, \frac{1}{2} ), sint=\frac{1}{2}, cost=\frac{\sqrt 3}{2}$
3. $( \frac{1}{2}, \frac{\sqrt 3}{2} ), sint=\frac{\sqrt 3}{2}, cost= \frac{1}{2}$
4. $(0,1), sint=1, cost=0$
5. $( - \frac{1}{2}, \frac{\sqrt 3}{2} ), sint=\frac{\sqrt 3}{2}, cost=- \frac{1}{2}$
6. $(- \frac{\sqrt 3}{2}, \frac{1}{2} ), sint=\frac{1}{2}, cost==\frac{\sqrt 3}{2}$
7. $(-1,0), sint=0, cost=-1$
8. $(- \frac{\sqrt 3}{2}, -\frac{1}{2} ), sint=-\frac{1}{2}, cost==-\frac{\sqrt 3}{2}$
9. $( - \frac{1}{2}, -\frac{\sqrt 3}{2} ), sint=-\frac{\sqrt 3}{2}, cost=- \frac{1}{2}$
10. $(0,-1), sint=-1, cost=0$
11. $( \frac{1}{2}, -\frac{\sqrt 3}{2} ), sint=-\frac{\sqrt 3}{2}, cost=\frac{1}{2}$
12. $(\frac{\sqrt 3}{2}, -\frac{1}{2} ), sint=-\frac{1}{2}, cost==\frac{\sqrt 3}{2}$
Work Step by Step
Start from $(1,0)$ and go counter clockwise, there are 12 points on the unit circle,
and their $(x,y), sint=y, cost=x$ can be found as the following:
1. $(1,0), sint=0, cost=1$
2. $( \frac{\sqrt 3}{2}, \frac{1}{2} ), sint=\frac{1}{2}, cost=\frac{\sqrt 3}{2}$
3. $( \frac{1}{2}, \frac{\sqrt 3}{2} ), sint=\frac{\sqrt 3}{2}, cost= \frac{1}{2}$
4. $(0,1), sint=1, cost=0$
5. $( - \frac{1}{2}, \frac{\sqrt 3}{2} ), sint=\frac{\sqrt 3}{2}, cost=- \frac{1}{2}$
6. $(- \frac{\sqrt 3}{2}, \frac{1}{2} ), sint=\frac{1}{2}, cost==\frac{\sqrt 3}{2}$
7. $(-1,0), sint=0, cost=-1$
8. $(- \frac{\sqrt 3}{2}, -\frac{1}{2} ), sint=-\frac{1}{2}, cost==-\frac{\sqrt 3}{2}$
9. $( - \frac{1}{2}, -\frac{\sqrt 3}{2} ), sint=-\frac{\sqrt 3}{2}, cost=- \frac{1}{2}$
10. $(0,-1), sint=-1, cost=0$
11. $( \frac{1}{2}, -\frac{\sqrt 3}{2} ), sint=-\frac{\sqrt 3}{2}, cost=\frac{1}{2}$
12. $(\frac{\sqrt 3}{2}, -\frac{1}{2} ), sint=-\frac{1}{2}, cost==\frac{\sqrt 3}{2}$
