What is the value of \text{cosec}(-\frac{73\pi}{3})?
- A. \frac{2}{\sqrt{3}}
- B. -\frac{2}{\sqrt{3}} ✓
- C. 2
- D. -2
Correct Answer: B. -\frac{2}{\sqrt{3}}
Explanation
\text{cosec}(-\frac{73\pi}{3}) = -\text{cosec}(\frac{73\pi}{3}) = -\text{cosec}(24\pi + \frac{\pi}{3}). Since sine is periodic with 2\pi, this evaluates to -\text{cosec}(\frac{\pi}{3}) = -\frac{2}{\sqrt{3}}.