1. The problem is to find the values of $\sin 60^\circ$, $\cos 60^\circ$, and $\tan 60^\circ$. 2. Recall the special angles in trigonometry: for $60^\circ$, the values are derived from an equilateral triangle split into two 30-60-90 right triangles. 3. The formulas for these angles are: - $\sin 60^\circ = \frac{\sqrt{3}}{2}$ - $\cos 60^\circ = \frac{1}{2}$ - $\tan 60^\circ = \frac{\sin 60^\circ}{\cos 60^\circ} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$ 4. Simplify $\tan 60^\circ$: $$\tan 60^\circ = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$$ 5. Therefore, the values are: - $\sin 60^\circ = \frac{\sqrt{3}}{2}$ - $\cos 60^\circ = \frac{1}{2}$ - $\tan 60^\circ = \sqrt{3}$ These are exact values commonly used in trigonometry.