Question

The solution of \( \sin x = \frac{-\sqrt{3}}{2} \) is:

• A. \( x = n\pi + (-1)^n \frac{4\pi}{3} \), where \( n \in \mathbb{Z} \)
• B. \( x = n\pi + (-1)^n \frac{2\pi}{3} \), where \( n \in \mathbb{Z} \)
• C. \( x = n\pi + (-1)^n \frac{3\pi}{3} \), where \( n \in \mathbb{Z} \)
• D. None of these

Hint:

Use the general solution for trigonometric equations to find all possible solutions in the specified domain.

Answer 1

The Correct Option is A

The general solution to the equation \( \sin x = \frac{-\sqrt{3}}{2} \) is derived using standard trigonometric identities. The solution is given by \( x = n\pi + (-1)^n \frac{4\pi}{3} \).
Final Answer: \[ \boxed{x = n\pi + (-1)^n \frac{4\pi}{3}, \text{ where } n \in \mathbb{Z}} \]