The expression evaluates to $\frac{\sqrt{3}}{2}$, which corresponds to one of the multiple-choice options.

Would you like more details on the steps involved, or do you have any questions?

Here are five related questions:

1. How do you simplify trigonometric expressions involving multiples of $\pi$?
2. What are the periodic properties of sine, cosine, and tangent functions?
3. How can you determine the sign of trigonometric functions based on the angle's quadrant?
4. What is the value of $\sin\left(\frac{35\pi}{6}\right)$ using reference angles?
5. Why is it important to simplify trigonometric expressions involving fractions of $\pi$?

Tip: When evaluating trigonometric functions for large angles, first reduce the angle using periodicity to a simpler reference angle.