Question

The interval of $x$ for which $cotx<0,(2\pi <x<4\pi )$ is:

• A. $x\in (\pi /2,3\pi )\cup (7\pi /2,4\pi )$
• B. $x\in (5\pi /2,3\pi )\cup (7\pi /2,4\pi ]$
• C. $x\in (5\pi /2,3\pi ]\cup (7\pi /2,4\pi )$
• D. $x\in (5\pi /2,3\pi )\cup (7\pi /2,4\pi )$

Answer 1

The correct option is D $x\in (5\pi /2,3\pi )\cup (7\pi /2,4\pi )$

From the graph, we can observe that the required interval is
$x\in (5\pi /2,3\pi )\cup (7\pi /2,4\pi )$