The sine and cosine of $30^\circ$ are well-known values in trigonometry:

• $\sin(30^\circ) = \frac{1}{2}$
• $\cos(30^\circ) = \frac{\sqrt{3}}{2}$

Let me know if you need more details or have any further questions! Here are some related questions to consider:

1. How do the sine and cosine values change for other common angles like $45^\circ$ and $60^\circ$?
2. Can you derive these values using the unit circle?
3. How does the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$ work with these values?
4. How do you compute sine and cosine using a calculator?
5. What are the applications of knowing these trigonometric values in real-world problems?

Tip: For angles like $30^\circ$, $45^\circ$, and $60^\circ$, memorizing the sine and cosine values can simplify many trigonometric problems.