1. **State the problem:** We need to find the values of $\cos(-3.45\pi)$ and $\sin(-3.45\pi)$ using the unit circle. 2. **Recall the unit circle properties:** On the unit circle, any angle $\theta$ corresponds to a point $(\cos \theta, \sin \theta)$. 3. **Simplify the angle:** Since angles on the unit circle are periodic with period $2\pi$, we reduce $-3.45\pi$ modulo $2\pi$: $$-3.45\pi + 2\pi = (-3.45 + 2)\pi = -1.45\pi$$ We can add $2\pi$ again to get a positive coterminal angle: $$-1.45\pi + 2\pi = ( -1.45 + 2)\pi = 0.55\pi$$ So, $-3.45\pi$ is coterminal with $0.55\pi$. 4. **Find coordinates for $0.55\pi$:** $0.55\pi$ radians is approximately $0.55 \times 180^\circ = 99^\circ$. Using the unit circle, the coordinates for $99^\circ$ are approximately: $$\cos(0.55\pi) \approx -0.16$$ $$\sin(0.55\pi) \approx 0.99$$ 5. **Therefore:** $$\cos(-3.45\pi) = \cos(0.55\pi) \approx -0.16$$ $$\sin(-3.45\pi) = \sin(0.55\pi) \approx 0.99$$ **Final answers:** $\boxed{\cos(-3.45\pi) = -0.16}$ $\boxed{\sin(-3.45\pi) = 0.99}$