Question

For any angle $x\in [-\frac{\pi }{4},\frac{\pi }{3}];\cot x\in$

• A. $(-1,\frac{1}{\sqrt{3}})$
• B. $(-\infty ,-1]\cup [\frac{1}{\sqrt{3}},\infty )$
• C. $[-\infty ,\frac{1}{\sqrt{3}})$
• D. $(-\infty ,-1)$

Answer 1

Answer: (B), (D)

$(-\infty ,-1)$

Given: $x\in [\frac{-\pi }{4},\frac{\pi }{3}]$ and for finding the range of $\cot x$ in this interval, let's use the graph of $\cot x$


From the graph, for $x\in [\frac{-\pi }{3},\frac{\pi }{4}]$

$\cot x\in (-\infty ,-1]\cup [\frac{1}{\sqrt{3}},\infty )$