9. Determine the value of $c$. a. $45^{\circ}$ b. $72^{\circ}$ c. $54^{\circ}$ d. $48^{\circ}$

Step 1 ：Let $P$ be the point on the unit circle that is $c$ counterclockwise from $(1,0)$, and let $D$ be the foot of the altitude from $P$ to the $x$-axis.

Step 2 ：Triangle $POD$ is an isosceles right triangle, so $DO = DP = \frac{\sqrt{2}}{2}$.

Step 3 ：Therefore, the coordinates of $P$ are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.

Step 4 ：So, $\tan c = \frac{\sin c}{\cos c} = \frac{\sqrt{2}/2}{\sqrt{2}/2} = 1$.

Step 5 ：Since $\tan 45^\circ = 1$, the value of $c$ is $\boxed{45^\circ}$.