To determine $\sin 60^\circ$, observe the symmetry in trigonometric functions between sine and cosine:

1. Sine and cosine are complementary, i.e., $\sin \theta = \cos(90^\circ - \theta)$ for any angle $\theta$.

   • For $\sin 60^\circ$, we use the complementary relationship: $\sin 60^\circ = \cos (90^\circ - 60^\circ) = \cos 30^\circ$

2. From standard trigonometric values, $\cos 30^\circ = \frac{\sqrt{3}}{2}$. Therefore: $\sin 60^\circ = \frac{\sqrt{3}}{2}$

Final Answer:

$\sin 60^\circ = \frac{\sqrt{3}}{2}$

---

Would you like a detailed explanation of trigonometric function symmetry or unit circle concepts? Here are some questions to deepen understanding:

1. Why are sine and cosine complementary functions?
2. How does the unit circle relate to trigonometric values of angles?
3. Can you derive $\sin 60^\circ$ geometrically using a 30°-60°-90° triangle?
4. What are the values of $\tan 60^\circ$ and $\cot 60^\circ$?
5. How do these values help in solving real-world problems involving angles?

Tip: Always refer to the unit circle or a right triangle for quick trigonometric value verification!