1. **Problem statement:** Find the exact values of $\sin x$ and $\cos x$ for a given angle $x$. 2. **Formula and rules:** The exact values of $\sin x$ and $\cos x$ depend on the angle $x$. Common exact values are known for angles like $0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, and $90^\circ$ (or in radians $0$, $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$, $\frac{\pi}{2}$). 3. **Important rules:** - $\sin^2 x + \cos^2 x = 1$ (Pythagorean identity). - Exact values for $\sin$ and $\cos$ at special angles: - $\sin 0 = 0$, $\cos 0 = 1$ - $\sin \frac{\pi}{6} = \frac{1}{2}$, $\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}$ - $\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$, $\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$ - $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$, $\cos \frac{\pi}{3} = \frac{1}{2}$ - $\sin \frac{\pi}{2} = 1$, $\cos \frac{\pi}{2} = 0$ 4. **Intermediate work:** Without a specific angle $x$, we cannot compute exact values. Please provide the angle $x$ to find $\sin x$ and $\cos x$. 5. **Explanation:** To find exact values of $\sin x$ and $\cos x$, you need to know the angle $x$. Then use the unit circle or special triangles to find these values exactly. **Final answer:** Please specify the angle $x$ to find exact values of $\sin x$ and $\cos x$.